Born in Los Angeles, Battey attended Jordan High School in the Watts neighborhood of Los Angeles. He was signed as an amateur free agent by the Chicago White Sox prior to the 1953 season. Battey was assigned to the Colorado Springs Sky Sox in the Single-A Western League where he began his baseball career by hitting only a .158 batting average in 26 games. The White Sox demoted him to the Waterloo White Hawks in the B-level Illinois–Indiana–Iowa League and Battey responded with a .292 average and 11 home runs in 129 games. In 1955, Battey was promoted to the Triple-A Charleston Senators in the American Association where, he hit for a .269 batting average along with 8 home runs and 71 runs batted in. His performance earned him a promotion to the major leagues where he made his debut with the White Sox on September 10, 1955 at the age of 20.
Battey returned to the minor leagues in 1956, playing in 36 games for the Toronto Maple Leafs. Despite hitting only .178, he played well defensively. The White Sox called him back to the major leagues to back up starting catcher Sherm Lollar, for the remainder of the season although, he spent the time on the bench and would only play in four games. Battey continued to learn from the perrenial All-Star Lollar during the 1957 season but struggled offensively. He was sent back to the minor leagues in August where he would hit 9 home runs and 20 runs batted in for the Triple-A Los Angeles Angels of the Pacific Coast League. The White Sox recalled Battey to the major leagues in September – this time to stay.
Battey would hit .226 along with 8 home runs in 1958 as, the White Sox would battle back from being in last place on June 14 to finish the season in second place behind the New York Yankees. In 1959 he was overtaken by rookie Johnny Romano as the second string catcher, ending the year hitting .219 in 26 games. Although the White Sox won the American League pennant, Battey wouldn't appear in the post-season as the White Sox lost to the Los Angeles Dodgers in the 1959 World Series.
Realizing they had a logjam at catcher with the veteran, and still productive, Lollar, the impressive rookie Romano, and the still-valuable-as-a-defensive-backup Battey, White Sox owner and general manager Bill Veeck would solve his problem in two deals that would show immediate dividends for the White Sox, but would be long term disasters. On December 6, 1959, Veeck traded Romano, rookie first baseman Norm Cash, and utility man Bubba Phillips to the Cleveland Indians for outfielder Minnie Miñoso, catcher Dick Brown, pitcher Don Ferrarese, and minor league pitcher Jake Striker. Then on April 4, 1960, Veeck would ship Battey, first baseman Don Mincher, and $150,000 to the Washington Senators for veteran first baseman Roy Sievers. Although both Sievers and Miñoso would combine for three 20-home run seasons, two All-Star appearances, one Gold Glove award in 1960 and 1961 with the White Sox, the rest of the players the team received in trade were largely of the replacement level. Conversely the young players that the Sox parted with (to get these veterans), namely Battey, Mincher, Romano, and Cash, would all sparkle, and account for 17 20-home run seasons, four 30-home run seasons, one 40-home run season, 12 all-star team selections, three Gold Gloves (all by Battey), and would garner Most Valuable Player support in numerous seasons. Meanwhile, the catcher that the White Sox chose to keep, Lollar, would go into decline after 1959, be relegated to a backup role in 1962, and would retire after the 1963 season, leaving the White Sox with an underwhelming starter catcher, including a two-year return of an aging Romano in 1965, before regaining some form of stability behind the plate in 1969 with Ed Herrmann (who would go on to lead the American League in passed balls in four of his six full seasons with the Sox).
Battey became the starting catcher for the Senators and began to show his defensive abilities, leading the American League in assists and putouts for four consecutive years from 1960 to 1963 but, it would be offensively where Battey would shine and start hitting as he had done in the minor leagues. Battey would go on to play in a then-career high 137 games and hit .270, with 15 home runs and 60 RBI. He would also earn his first Gold Glove Award and finish eighth in the 1960 American League Most Valuable Player Award. In October, Battey was named to the United Press International's American League All-Star team.
Prior to the 1961 season, the Senators relocated to the Minneapolis-St. Paul metro area and were renamed the Minnesota Twins. Battey would team with future Baseball Hall of Fame member Harmon Killebrew, future MVP Zoilo Versalles, and All-Stars Bob Allison, Camilo Pascual, and Jim Kaat to form the nucleus of a pennant-winning team in Minnesota. Building on his breakout 1960 season, Battey ended 1961 with a .302 batting average, sixth best in the American League, and won his second Gold Glove Award.
Battey was recognized as one of the top catchers in the major leagues when he was selected to be the starting catcher for the American League in the 1962 All-Star Games. He was the Twins catcher on August 26, 1962, when pitcher Jack Kralick threw a no-hitter. Battey appeared in a career-high 148 games and ended the season with a .280 batting average, highest among major league catchers. He also set a record for major league catchers by picking off 15 base runners as he won his third consecutive Gold Glove Award. The Twins, long an American League doormat while in Washington, would finish a surprising second in the American League standings with 91 wins (5 games behind the World Series winning New York Yankees.
Battey would have his finest season at the plate in 1963, hitting .285 while setting career highs in home runs (26), RBI (84), and slugging percentage (.476). He would also be voted to his second straight All-Star team (where he would collect his only all-star hit, a third-inning single that scored Boston Red Sox third baseman Frank Malzone from secondbase to tie the game at 3-3), and finish seventh in the American League Most Valuable Player Award balloting (behind Killebrew and winner and fellow catcher Elston Howard). The Twins would again finish with 91 wins but, this time it would put them no better than third place, 15½ games behind the World Series runner-up Yankees. Both Battey and the Twins would take a step backward in 1964 with the team struggling to a 79 win, sixth-place finish in the American League while Battey would hit .272 with 12 home runs and 51 RBI in 131 games.
Battey recovered in 1965 and was hitting near .300 at mid-season when he received the most All-Star votes by an American League player for the 1965 All-Star Game which was played in his home ball park, Metropolitan Stadium. He was one of six Twins to appear in the 1965 mid-season classic (with Versalles, Killebrew, Jimmie Hall, Mudcat Grant, and Tony Oliva). Battey was an integral member of the Twins team that went on to clinch the American League pennant, hitting for a .297 batting average and finished in tenth place in voting for the American League Most Valuable Player Award (with teammate Versalles winning and six Twins finishing in the top 15). He started every game in the 1965 World Series but only hit for a .120 average with 2 RBI and only one extra base hit as the Twins lost to the Los Angeles Dodgers in a seven-game series.
In 1966, Battey hit .255 with 4 home runs and 31 RBI while playing in 115 games, his lowest total since his backup days in Chicago. Battey was selected for his fourth and last All-Star game, coming into the game in the bottom of the sixth inning for starter, Tiger catcher Bill Freehan.
The 1967 season would be Battey's last as he battled a thyroid condition that caused him to gain weight. He would appear in only 48 games and hit for just a .165 average. The Twins three catchers that season, Battey, Jerry Zimmerman, and Russ Nixon, combined to only hit .176 and the Twins went 2-5 in late September and lost the pennant to the Red Sox in the last game of the season.
In a thirteen-year major league career, Battey played in 1,141 games, accumulating 969 hits in 3,586 at bats for a .270 career batting average along with 104 home runs and 449 RBI. He led the American League four times in assists and putouts, three times in baserunners caught stealing and twice in caught stealing percentage, with a career fielding percentage of .990. A four-time All-Star, Battey won three Gold Glove Awards. Over his career, he threw out 43.44% of the base runners who tried to steal a base on him, 15th on the all-time list. In 1961, the reigning American League stolen base champion, Luis Aparicio, rated Battey as the toughest catcher on which to attempt a stolen base.
Richard Kendall of the Society for American Baseball Research devised an unscientific study that ranked Battey as the seventh most dominating fielding catcher in major league history. Battey played more games at catcher than any other player in Twins history (831). He was named to the Twins' 40th anniversary team in 2000. Battey was one of the first Major League players to wear an earflap on his batting helmet in 1961 after twice suffering broken cheekbones when hit by pitches.
After his playing career, he next spent 12 years working in New York City as a recreation specialist with young disturbed boys. Fulfilling a promise he had made to his mother, Battey enrolled at Bethune-Cookman University in 1980. Taking 34 credits a semester, he finished his undergraduate degree in Education in 2½ years, while coaching the men's basketball team, and was accorded the distinction of Summa Cum Laude honors. After graduating from Bethune-Cookman, he became a high school teacher and baseball coach in Ocala, Florida.
Battey was also part of a charity program sponsored by Consolidated Edison whereby children were given free bleacher tickets to New York Yankee games. He talked baseball and was a "big brother" to all the kids who were lucky enough to benefit from the program. Battey died of cancer at the age of 68 in Ocala, Florida.
In 2004, Battey was posthumously elected to the Twins Hall of Fame. In 2010, the Twins celebrated their 50th season in Minnesota and Battey was voted as one of the 50 Greatest Twins Players.