Bergen was reassigned to Triple-A El Paso on Tuesday.
Bergen signed with the Padres as a non-roster invitee Friday, Jeff Sanders of The San Diego Union-Tribune reports.
Bergen went unclaimed on waivers and was assigned Monday to Triple-A Buffalo.
Bergen was designated for assignment by the Blue Jays on Tuesday, Mitch Bannon of SI.com reports.
Bergen (shoulder) was activated from the 10-day injured list Wednesday and subsequently optioned to Triple-A Buffalo.
Bergen (shoulder) threw 20 pitches of live batting practice Tuesday, Keegan Matheson of MLB.com reports.
Bergen was placed on the 10-day injured list with a left shoulder impingement Thursday.
Bergen was credited with a blown save Sunday against the Rays. He issued three walks in one-third of an inning.
Bergen (1-0) allowed no hits and a walk in one scoreless inning to earn the win against Atlanta on Thursday.
Bergen fired a perfect first inning Saturday in the win over Atlanta. He did not factor in the decision.