Meacham was originally drafted by the Chicago White Sox out of Mater Dei High School in Santa Ana, California in the 14th round of the 1978 Major League Baseball Draft, but chose, instead, to play baseball at San Diego State University.
He earned third team All-America accolades as a freshman, and was named San Diego State Aztecs team MVP in 1979. He was second team All-American in 1981 after batting .375 with seven home runs, 51 runs batted in and 44 stolen bases, and was selected by the St. Louis Cardinals with the eighth overall pick in the 1981 Major League Baseball Draft. He signed, ending his college career as SDSU's all-time leader in runs (214), hits (277) and at bats (767), and was second in career stolen bases (116), including a streak of thirty consecutive.
Baseball Hall of Fame member Tony Gwynn credited Meacham for helping him join the San Diego State Aztecs baseball team after coming to the school on a basketball scholarship. The two played against each other in high school and Meacham, knowing Gwynn's abilities well, encouraged Coach Jim Dietz to give him an opportunity.
Meacham batted only .182 for the Gastonia Cardinals of the South Atlantic League in 1981. His batting average improved to .259 in 1982 with the Florida State League's St. Petersburg Cardinals, but his .915 fielding percentage and 47 errors was far worse than the organization that employed Ozzie Smith at short was used to. On December 14, 1982, he was traded to the New York Yankees with OF Stan Javier for P Marty Mason, P Steve Fincher and OF Bob Helsom in a minor league deal.
This turned out to be a very good deal for the Yankees, as none of the three players the Yankees sent to the Cardinals ever reached the majors, and Javier was later included in the December 5, 1984 deal to acquire Rickey Henderson from the Oakland Athletics. Meacham, meanwhile, earned a major league promotion by June of his first season with his new club. He made his Major League debut on June 30 in the 12th inning of an extra innings game against the Baltimore Orioles. The Yankees won on a Butch Wynegar walk off home run before Meacham could log his first major league at bat. That didn't occur until his third Major League game against the Seattle Mariners on September 3, 1983. He lined out to Mariners third baseman Manny Castillo. By the end of the season, Meacham had won the Yankees' starting shortstop job, appearing in a total of 22 games, and batting .235 in 51 at bats.
During the off season, the Yankees acquired Tim Foli to play short in 1984. The Yankees ended up having something of a revolving door at short, with Meacham, Foli, Roy Smalley and Andre Robertson all seeing playing time at the position. Meacham emerged with the most playing time of the bunch, logging 840 innings and batting .253 with two home runs and 25 RBIs. Despite his limited role, Meacham led the American League with 14 sacrifice hits for the season. Meacham was the Yankees regular shortstop in 1985, playing in 156 out of 162 games. He hit just .218 in 1985 but led the major leagues with 23 sacrifice hits.
The most notable play of Meacham's career was a bizarre baserunning gaffe which also involved Dale Berra in an 11-inning 6–5 loss to the Chicago White Sox at Yankee Stadium on August 2, 1985. With Meacham and Berra the runners at second and first base respectively in the seventh inning of a game tied at three, Rickey Henderson hit a ball that rolled to the farthest reaches of left-center field. When Meacham slipped between second and third base, both runners ended up approaching home plate in synchronized fashion, one on the heels of the other. After catching the relay throw from shortstop Ozzie Guillén, catcher Carlton Fisk tagged out Meacham to his right, then turned to his left just a split second later to do the same to Berra to complete the double play. Yankees manager Billy Martin commented, "I've never seen that in grammar school, much less a major-league game."
The Yankees were growing frustrated with Meacham's generally inconsistent play, and had acquired both Paul Zuvella and Wayne Tolleson in separate deals during the 1986 season to replace him at short. Meacham ended up splitting 1986 and 1987 between the Yankees and their triple A affiliate, the Columbus Clippers. He spent all of 1988 with the big league club, but injuries and the off season acquisition of Rafael Santana from the New York Mets limited Meacham to only 47 games, during which, he saw about half his playing time at second base.
Yankees owner George Steinbrenner was particularly frustrated with Meacham's injuries and lackluster play and often lambasted him in the New York press. Following the 1988 season, Meacham was traded to the Texas Rangers for Bob Brower.
Meacham failed to make the Rangers out of Spring training 1989, and was released by the club. He joined the Pittsburgh Pirates shortly afterwards, spending all of the 1989 season with their triple A affiliate, the Buffalo Bisons, but never reaching the major league level. He spent 1990 with the Omaha Royals, but again failed to make the major league club, however, following his retirement as a player, Meacham received his first minor league coaching job from the Kansas City Royals.
After serving as a minor league coach with the Colorado Rockies in 1993 and the Pittsburgh Pirates from 1994 to 2001, Meacham was given his first managerial job in 2002 with the Rancho Cucamonga Quakes (advanced A California League affiliate of the Anaheim Angels). He held that job through 2004, and returned to the Rockies organization in 2005 as their Minor League roving infield instructor. The following season, he received his first major league coaching job, when new Florida Marlins manager Joe Girardi named him third base coach in 2006.
Meacham was the San Diego Padres first base coach for the 2007 season, and rejoined Girardi as the Yankees' third base coach for 2008, however, on October 14, 2008, it was announced that Meacham's contract would not be renewed for the 2009 season. Meacham spent 2009 with the Philadelphia Phillies organization, as the batting coach for the Williamsport Crosscutters. On October 30, 2009, he was hired as the first base coach for the Houston Astros under new manager Brad Mills.
On August 19, 2012, Meacham was released from the Houston Astros, along with Manager Brad Mills and hitting coach Mike Barnett.
He was announced as the manager for the Dunedin Blue Jays on January 7, 2013.
On January 13, 2014, Meacham was named as the manager for the Toronto Blue Jays Double-A affiliate New Hampshire Fisher Cats.
On November 28, 2016, the Blue Jays promoted Meacham to be manager of their Triple-A affiliate Buffalo Bisons.
Meacham and his wife, Gari, have three children. The Meachams gained notoriety in 1985 when Yankees manager Billy Martin and owner George Steinbrenner attempted to refuse to give Meacham a day off to witness the birth of his first child.