Hendry, who was the Cubs GM from 2002-11, was let go by chairman Tom Ricketts after two straight fifth-place finishes.
Cashman said he believes Hendry will be an invaluable resource.
"He can scout amateur players; he scouts pro players for us," he said. "He's as connected in the game as you can possibly be. Everybody loves this man."
Hendry, 56, worked 17 years in the Cubs organization in numerous positions, including farm director, scouting director, assistant GM and GM.
Hendry agreed to a multiyear deal with the Yankees, according to a source. Another source said Hendry's duties will include looking at minor league players, major league players and spending time with the major league team.
"We are excited to have someone with Jim's baseball knowledge, character and background join our baseball operation department," Yankees assistant GM Billy Eppler said. "Whenever you can add someone with his level of experience you have without a doubt advanced your efforts."
Under Hendry's direction the Cubs won three division titles (2003, 2007, 2008). The 2003 team was five outs away from the franchise's first World Series appearance since 1945 before an eighth-inning implosion in Game 6 against the Marlins in the NLCS.
New York also promoted Steve Donahue to head athletic trainer on Tuesday. He succeeds Gene Monahan, who retired after 39 seasons as head trainer and 49 with the Yankees overall. Mark Littlefield, who had been the Yankees' head minor league athletic trainer, becomes assistant athletic trainer with the big league team.
Assistant general manager Jean Afterman was given the additional title of senior vice president
Eppler was promoted from senior director of professional personnel to an assistant GM and Will Kuntz becomes manager of pro scouting, up from pro scouting assistant.
Bruce Levine covers the Cubs for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.