Brennan was claimed off waivers by the Red Sox on Monday and optioned to Triple-A Worcester.
Brennan will get to stick around on a 40-man roster after getting designated for assignment by the Mariners on Wednesday, though he won't be making his season debut just yet. He owns a respectable 4.45 ERA in 54.2 innings at the major-league level over the past two seasons, so he can probably fill at least a low-leverage role for the Red Sox at some point. Ryan Brasier (calf) was transferred to the 60-day injured list in a corresponding move.