Henrich died Tuesday in Dayton, Ohio, the Yankees announced. No cause of death was given.
A five-time All-Star outfielder, he joined the Yankees in 1937 and played until 1950, winning four World Series championships. He missed three seasons while serving in the Coast Guard during World War II.
Henrich hit the first game-ending home run in World Series history, leading off the bottom of the ninth inning with a drive against Don Newcombe to beat the Brooklyn Dodgers, 1-0, in the 1949 opener.
"If we were ahead 10-1 or 10-2, he was just average. If we were behind 10-1 or 10-2, same thing. But get him in a big game and he was terrific. We didn't call him 'Old Reliable.' We just knew he was 'Old Reliable,' " said former teammate Bobby Brown.
Yet Henrich's most famous at-bat might have been a time when he didn't hit the ball. In Game 4 of the 1941 World Series against the Dodgers, Henrich struck out to seemingly end the game. But Brooklyn catcher Mickey Owen dropped the third strike and Henrich raced safely to first base. Given another chance, the Yankees rallied for four runs in the ninth inning for a 7-4 win and a 3-1 series edge.
Henrich hit .282 with 183 home runs and 795 RBIs. He hit a career-high 31 home runs in 1941 and had 100 RBIs in 1948.
He played in the World Series in 1938, 1941, 1947 and 1949, and won championships every time. He hit one home run in each series.
Yogi Berra, Joe DiMaggio, Whitey Ford and Lou Gehrig were among his Hall of Fame teammates.
Henrich was born Feb. 20, 1913, in Massillon, Ohio, a city known for its football prowess, and was longtime friends with famed football coach Paul Brown.
After retiring, Henrich was a coach with the Yankees, New York Giants and Detroit Tigers.
"Being around Tommy made you feel good, whether playing cards or listening to him sing with that great voice," Berra said in a statement released by the Yankees. "He was a proud man, and if you knew him, he made you proud too."
A private memorial service is scheduled Saturday.