Outman was acquired from Cleveland on Thursday. His contract was selected from Triple-A Scranton/Wilkes-Barre before Friday night's game at Toronto.
Outman went 4-0 with a 3.28 ERA in 31 relief appearances with the Indians this season, but was sent to the minors in June. The six-year veteran also has pitched for Oakland and Colorado.
Hill, who began the season with the Los Angeles Angels, had no record and did not allow a run in six games with the Yankees.
The Yankees have used 52 players this season, the second-highest total in team history. They used 56 last year.