Sportsnet 650's Chad Dey was first to report on the agreement early Wednesday morning.
The team made the deal official on Wednesday night.
— Red Sox (@RedSox) December 2, 2021
The 33-year-old Paxton, from Ladner, B.C., suffered a left elbow injury in his first start with the Seattle Mariners in 2021 and then underwent season-ending Tommy John surgery.
The six-foot-four former ace returned to the Mariners for a second stint in 2021 after signing a one-year, $8.5-million deal.
Paxton is 57-33 with a 3.59 ERA in his nine-year major league career with the Mariners and New York Yankees.
Paxton will become the second Canadian pitcher on the Red Sox, joining Victoria's Nick Pivetta.