Rapada, 30, will step into the competition for a roster spot as a lefty specialist after 36-year-old Hideki Okajima was unable to pass a physical this week, voiding the veteran's Minor League deal.
Released by the Orioles this week, Rapada went 2-0 with a 6.06 ERA in 32 appearances for Baltimore last season, permitting 11 runs on 14 hits in 16 1/3 innings. He walked seven and struck out 18.
Originally signed by the Cubs as an undrafted free agent in 2002, Rapada has compiled a career 5.13 ERA with a 5-0 record in 78 appearances with Chicago (2007), the Tigers (2007-09), the Rangers (2010) and Baltimore.
He has held left-handed hitters to a .153 (18-for-118) batting average in his Major League career, including a .090 (6-for-67) mark over the last two seasons -- the best such mark against left-handed hitters over that stretch for pitchers with a minimum of 70 batters faced.
The Yankees are evaluating low-risk options to add a second left-handed reliever behind Boone Logan, a role that largely went unfilled last season. New York will also take looks at Cesar Cabral, Juan Cedeno and Mike O'Connor for that role.