Kearns, hitting .272 with eight home runs and 42 RBIs this season, signed a Minor League contract with the Indians this offseason and made the big club in Spring Training.
The nine-year Major League veteran, who was set to become a free agent this offseason, was pulled from Friday's contest for a pinch-runner after singling in the seventh frame.
"At first, when I came out I thought something might be up," Kearns said. "I thought maybe I was just getting [some rest] late in the game. [We were] down some so -- I didn't really know."
With Saturday's 4 p.m. ET non-waiver Trade Deadline looming, general manager Mark Shapiro said this was not a spur of the moment deal, and that he had been in constant communication with the Yankees over the past few weeks.
As for the player to be named, who must be selected on or before Aug. 20, Shapiro said he has a small group of players to choose from. He did not reveal any of the names in the group, only that "it will be a player we like and who has Major League value."
Indians manager Manny Acta coached Kearns for two and a half seasons in Washington (2007-09), before reuniting with the outfielder in Cleveland. He had encouraging words for the 30-year-old.
"I can't say enough about what this guy has done for us," Acta said. "Me being familiar with him, I have a soft spot for this guy -- spending two and a half years with him over there in D.C. He came over here in Spring Training with no spot guaranteed or anything for the first time in his career. He earned the spot and pretty much carried this club for a month or so when Grady Sizemore went down and some of the other guys were struggling.
"We wish him the best. I think this guy has paid his dues and he deserves to go to a contender at this time in his career and maybe a chance to win a ring."
Kearns, saddened to leave his teammates, was also excited for the opportunity to go to a contender.
"That's why we play," he said. "That's why we all play -- to win."
James Hall is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.