Cook was pitching for Triple-A Nashville but has been a key member of Oakland's bullpen in the past, even making four appearances for the A's early in the year.
"This is a guy that's been a closer in the past," Red Sox manager John Farrell said. "You look at guys that have had success in the past. You're looking for the potential of a bounce back, not so much in the immediate timeframe, but how could that play into the construction of a bullpen going into next year."
A's manager Bob Melvin praised Cook for his contributions to Oakland's success the past three years.
"He comes in and all of a sudden he's a closer and an All-Star," Melvin said. "He's been pretty good for us the last three years. A change of scenery will do him some good."
Also Friday, Oakland acquired left-hander Felix Doubront from Toronto for cash after he was designated for assignment by the Blue Jays on Wednesday. Melvin said he expects Doubront to join the team on Saturday.
"He's a big guy with an assortment of pitches," Melvin said. "He's been a starter and we'll see how it goes in the coming days."
Cook was 4-1 with eight saves and a 4.05 ERA in 30 relief appearances this season with Triple-A Nashville. He was with Oakland from April 26 to May 2 and went 0-2 with a 10.38 ERA.