The 29-year-old right-hander last played for the Detroit Tigers, and elected to become a free agent after being designated for assignment on August 7.
An All-Star for the St. Louis Cardinals just four seasons ago, Rosenthal has struggled to regain his previous form after missing the entire 2018 season while recovering from Tommy John surgery. Over parts of seven seasons with three different clubs (Cardinals, Nationals, Tigers), Rosenthal owns a career ERA of 3.46 across 340 1/3 career innings. 
The Yankees will be hoping he can resemble the pitcher he was during the first six years of his career rather than the last one, but in all likelihood he'll serve as a minor league depth option in case anything goes awry with bullpen injuries down the stretch.
The Yankees kick off a nine-game road trip Tuesday night in Oakland looking to maintain their MLB-best .659 winning percentage as the regular season winds to a close.