McDonald was designated for assignment by the Red Sox on Saturday. He will join the Yankees on Friday for the start of a four-game series at Fenway Park.
McDonald appeared in 38 games and hit .214 with two homers and nine RBIs. The Yankees will make a corresponding 25-man roster move Friday.
To make room on the 40-man roster, New York designated pitcher Chris Schwinden for assignment. The right-hander had been claimed off waivers from Cleveland last Friday.
The moves were announced before the Yankees game Wednesday at Tampa Bay.