In 1966, he was named the American League Pitcher of the Year by The Sporting News, but the National League's Sandy Koufax won the Cy Young Award by a unanimous vote; it was the last year in which only one award was given for both leagues. Kaat was primarily a starting pitcher until 1979, when he became a relief pitcher.

Over Kaat's 25 years in the majors, he was an All-Star three times (1962, 1966, 1975), and won the Gold Glove Award for defensive skill a record 16 consecutive times (1962-1977). With the Cardinals in 1982, Kaat earned his only World Series ring working out of the bullpen. In 1983 he became the last major league player to have played in the 1950's to retire.

Upon retirement, he served a short stint with the Cincinnati Reds as the club's pitching coach. When Pete Rose took over in 1984 as the Reds' player/manager, he made good on a promise to Kaat, his former Philadelphia Phillies teammate, and hired the former hurler for his coaching staff. Kaat would coach part of the 1984 season and all of 1985, a year in which he guided Cincinnati rookie Tom Browning to a 20-9 record. "At least I can say I had a 20-game winner every year I coached," Kaat used to joke.

Kaat has also had a successful career as a broadcaster after retiring from baseball. From 1990-1993, Kaat served as an analyst for CBS television, teaming with Dick Stockton and then, Greg Gumbel in 1993; Kaat covered three World Series Trophy presentations for CBS (1990-1992). In 1995, he was nominated for an Emmy Award for "On Camera Achievement". Also in 1995, Kaat called the American League playoffs with Brent Musburger for ABC. In addition, he was on the team which won the "Outstanding Live Sports Coverage - Single Program" New York Emmy for covering Dwight Gooden's no-hitter and David Wells' perfect game.

He is currently an announcer for Yankees games on the YES Network, where his straight-shooting style is much in the mode of former Yankees broadcasters Tony Kubek and Bill White.