Cook lived most of his life in Chillicothe, Ohio, where he played baseball, basketball and football at Chillicothe High School.
He played collegiately at the University of Cincinnati, once throwing for 554 yards in a game. He was drafted by the Cincinnati Bengals in the first round of the 1969 NFL/AFL Draft after Bengals coach and founder Paul Brown saw Cook's performance in the Bearcats' come-from-behind, 23–21 victory against Miami University in Bo Schembechler's last game before he left to coach at the University of Michigan. Brown had attended the game, but left when the Miami Redskins' lead reached 21–6. "That quarterback. That's our draft choice," said Brown after seeing film of Cook's rallying performance.
In 1969, the Bengals released John Stofa, the Bengals' starting signal caller for much of the team's inaugural season, and named Cook as the starting quarterback. His season started spectacularly, as he led the Bengals to a 3–0 record. However, in game three versus Kansas City, Cook felt a pop in his right (throwing) shoulder after being tackled by linebacker Jim Lynch and missed the next three games. Possibly due to the limited medical technology at the time, his torn rotator cuff went undiagnosed.
Despite this, Cook went on to pass for 1,854 yards and led the Bengals to wins over the Chiefs and the Oakland Raiders, two of the three best teams in the AFL. His 9.411 yards per pass attempt and 17.5 yard per completion are rookie records that still stand. Cook was UPI's choice for AFL Rookie of the year.
Cook recalled, "I took cortisone shots and played in pain, but the shoulder hadn't started to deteriorate yet, so I could still function. I still had the strength. I felt obligated to finish the season. I'd gotten off to a good start. I didn't want to relinquish that."
The rotator cuff began deteriorating after the season; during surgery, it was revealed that Cook also had a partially detached biceps muscle. After three operations proved futile, he retired. A 1973 comeback attempt failed and Cook retired permanently. The NFL Network NFL Top Ten series named Cook the #1 One Shot Wonder in NFL history.
Miami Dolphins quarterback Chad Pennington, who suffered two tears to his rotator cuff and has undergone as many surgeries to repair it, is often compared to Cook because their injuries are so similar; his injury was also similar to that suffered by New Orleans Saints quarterback Drew Brees, who had surgery on his rotator cuff after the 2005-06 season and finished the following season as an All-Pro quarterback. Brees went on to lead the Saints to victory over Indianapolis in Super Bowl XLIV.
Cook finished his career with 1,865 passing yards with an average of 17.4 yards per completion. He threw 15 touchdowns in his career and 11 interceptions.
Following retirement, Cook lived in Cincinnati, and worked with United Parcel Service and with Worksite Information Network as a motivational speaker for labor unions. He was an art major at the University of Cincinnati, and continued to paint. Cook had works on display in the Ohio Governor's Mansion. Cook did some color commentary of University of Cincinnati football broadcasts in the mid-1980s.
Cook died on January 27, 2012, shortly after being admitted to The Christ Hospital, a Cincinnati-area hospital, with pneumonia.