Tillman was recalled from Triple-A Norfolk to start the first game of Saturday's day-night doubleheader against the New York Yankees.
Baltimore will need to make a roster move between games as well in order to create a spot for Zach Britton. The left-hander is slated to start the nightcap against Yankees rookie Ivan Nova, also coming back from the minors.
Bergesen left the team to be with his wife for the birth of their first child. He can remain on the paternity leave list for a maximum of three days.
The right-hander is 2-7 with a 5.79 ERA in 20 games, including 12 starts.