A San Francisco Bay area product, Biagini was drafted by the Giants in 2011 from the University of California. Claimed by the Blue Jays in the 2015 Rule 5 draft, the righthander spent four years toiling in Toronto, posting a 14-24 record with a 4.86 ERA, mostly in relief.

Biagini was sent with pitcher Aaron Sanchez to Houston at the 2019 trade deadline for Derek Fisher and a minor leaguer. In 13 appearances, he was 0-1 with a 7.36 ERA before getting sent to the minors. Nonetheless, he is expected to be bullpen depth for the Astros in 2020.