Hill earned a hold against Texas on Tuesday by retiring both batters he faced, striking out one.
The Yankees signed Hill to a one-year contract Thursday, Jeff Passan of ESPN.com reports.
The White Sox released Hill on Tuesday.
The White Sox designated Hill for assignment Wednesday.
Hill signed a one-year, $1.8 million contract with the White Sox on Thursday, Jeff Passan of ESPN.com reports.
Hill (finger) was transferred Friday from the 15-day injured list to the 60-day injured list.
Hill underwent surgery Wednesday to repair ligaments and clean up scar tissue in his left ring finger, Jeff Sanders of The San Diego Union-Tribune reports.
The Padres placed Hill on the 15-day injured list Monday with a sprained left ring finger.
The Padres reinstated Hill (finger) from the 15-day injured list Friday.
Hill (finger) started a minor-league rehab assignment with Single-A Lake Elsinore on Friday, allowing six runs (five earned) on seven hits and no walks while striking out one batter over two-thirds of an inning.