The Boston Globe first reported the agreement.
A source told ESPN's Adam Schefter that Hoyer's contract with the Patriots is for $1.05 million. He is making $2 million from the Indianapolis Colts, who released him on Saturday, so with offset language, Hoyer will make $2 million in guarantees total this season between the two teams.
Stidham beat out Hoyer for the No. 2 job last preseason, which led the Patriots to release Hoyer with hopes of possibly bringing him back later in the season. But the Colts, who were scrambling after Andrew Luck's retirement, quickly scooped Hoyer up by inking him to a three-year contract to back up Jacoby Brissett.
Hoyer, 34, becomes the most experienced quarterback on the Patriots' roster (38 career starts), and should be a valuable sounding board for Stidham as the Patriots assess if the youngster can fill the void created by Tom Brady signing with the Tampa Bay Buccaneers.
Hoyer appeared in four games last season and made one start when Brissett suffered a knee injury. He completed just 53.8% of his pass attempts last season, throwing for 372 yards with four touchdowns and four interceptions.
Hoyer started his career with the Patriots and also had stints with the Cardinals, Browns, Texans, Bears and 49ers before returning to New England last season. He has 38 starts in 69 NFL games. He started 13 games for the Browns in 2014. He has thrown for 10,274 yards with 52 touchdowns and 34 interceptions in his career.
In addition to Hoyer, the Patriots also reached agreement with free-agent linebacker Brandon Copeland on a one-year, $1.05 million contract.
The 6-foot-3, 268-pound Copeland has played in 60 career regular-season games with the Detroit Lions (2015-2016) and New York Jets (2018-2019). He started 14 games for the Jets over the past two seasons, with his most notable success coming in 2018 as a situational pass-rusher (5 sacks). He has totaled 107 career tackles, while also factoring prominently on special-teams units.