Judge, who signed a nine-year $360 million deal this month to stay in New York, became the Yankees' 16th captain and first since Jeter, who held the title from 2003-14.
"Getting a chance to be the captain of the Yankees now, that goes without saying what an honour that is," Judge said.
"This is an incredible honour that I don’t take lightly."
The honour followed one of the greatest seasons ever seen at the plate as Judge slammed an American League record 62 home runs.
The towering right-handed outfielder has spent his entire career in Yankees pinstripes, becoming one of Major League Baseball's most feared sluggers after hitting 52 homers in his first full season to earn AL rookie of the year honours.
The Yankees also announced the acquisition of pitcher Carlos Rodon (30) on a six-year deal worth $162million.