Ramirez was designated for assignment by the Yankees on Feb. 28 to make room for Chan Ho Park.
In 20 relief appearances for the Yankees last season, Ramirez had 22 strikeouts in 22 innings. He was 5-1 with a 3.55 ERA and 63 strikeouts in 55 1-3 innings for New York in 2008, when his 10.3 strikeouts per nine innings was the seventh-best rate among AL relievers.
Ramirez was originally signed by the Los Angeles Angels as an undrafted free agent in February 2001.
The Rangers added Ramirez to their 40-man roster Tuesday. They didn’t have to make a corresponding move because they had only 39 players on the list before Ramirez.