The 32-year-old Kotsay hit .289 with six home runs and 37 runs batted in 88 games with the Braves.
He was scratched from Tuesday night's starting lineup, raising speculation that a trade was pending. Kotsay then pinch hit and walked in the ninth inning.
"I'd have to say it's my weirdest night as a professional in the big leagues," Kotsay said after the game. "I've never been scratched for that type of reason.
"I knew there was a possibility, so it wasn't a complete shock when I got called in and was told I would be scratched from the lineup due to precautionary reasons. The club was in discussions for possibly moving me."
Kotsay thought ahead to possibly joining the Red Sox.
"If that's the case, if I'm moved to a club that has postseason possibilities, you can't be disappointed as a player," he said. "I've had a lot of fun here and I've been happy with Bobby (Cox) and the organization."
The Braves acquired minor league outfielder Luis Sumoza in the deal. The 20-year-old hit .301 in 51 games for Class A Lowell of the New York-Penn League this season.
Atlanta obtained Kotsay from Oakland on Jan. 14. Coming off back surgery, he hit only .214 with one homer in 56 games for Oakland last year.
Kotsay has a .282 career batting average with 109 homers and 597 RBIs.