FOXBOROUGH, Mass. — Tom Brady didn’t go without a backup for long.

The New England Patriots signed former 49ers quarterback Brian Hoyer to a three-year deal on Wednesday, a day after Hoyer was released by San Francisco following its acquisition of Jimmy Garoppolo in a trade with New England.

Hoyer began his career as Brady’s backup in New England in 2009 and has spent time with seven teams during his nine-year career.

He started the first six games this season for the 49ers before being benched for C.J. Beathard. Hoyer now returns to back up a quarterback in Brady who has been one of the most durable in the league.

Offensive coordinator Josh McDaniels said he anticipates Hoyer will take full advantage of New England’s bye week to get up to speed on the playbook.

“Brian’s a smart guy. He’s got obviously some years in our system and our terminology,” McDaniels said. “It will be kind of a cram session here but I don’t expect that to take forever.”

Hoyer, 32, who has played in 55 games with 37 starts, has completed 833 of 1,404 passes (59 percent) for 9,853 yards with 48 touchdowns and 30 interceptions.

McDaniels said he wishes nothing but the best for Garoppolo.

“Every player wants to play. I understand that,” he said. “He had a few opportunities here and he did a good job with them, which is why he’s earned the opportunity that he has now.”

Now the Patriots will move forward with Hoyer.

“He’s a really smart kid,” McDaniels said. “He’s a football kid. He’s all about football and loves the game, cares about playing quarterback the right way, smart guy, works hard, good teammate, so there’s a lot to like. I spent a short amount of time with him. Looking forward to working with him here going forward in the second half of this season.”

Nonetheless, losing Garoppolo stung. McDaniels enjoyed working with him and saw his potential up close.

“We understand the business side of it, but the human element is you had a guy in your room that you really enjoyed being around,” McDaniels said. “I wish him nothing but the best. I really, really think a lot of this guy. He’s got a bright future, he’s a great person and I hope he does well for himself out there.”

IT DIDN’T look good when receiver Chris Hogan left the locker room Sunday with his right arm in a sling, suffering a shoulder injury following a reception with 3:21 left against the Los Angeles Chargers.

But the news Tuesday was about as encouraging as could be expected: An MRI on Monday revealed Hogan, per Ian Rapoport of the NFL Network, reportedly “does not need surgery for his shoulder injury,” just rest and rehabilitation. The expectation is Hogan will be out a couple of weeks, although he’ll be re-evaluated next week.

Not counting special teams captain Matthew Slater, that leaves the Patriots with three healthy receivers on their 53-man roster in Brandin Cooks, Danny Amendola and Phillip Dorsett. They do have the option of activating Malcolm Mitchell off injured reserve, assuming his cranky knee is OK.

Now in his fifth season, Hogan has only missed one game in his NFL career. That was for a bad back last season, his first with the Patriots.

Hogan has appeared in all eight games this season, making seven starts and playing 90.2 percent of the offensive snaps. He’s tied for third on the team in receptions (33), is third in receiving yards (438) and tied for first in receiving touchdowns (5).

Hogan has been especially impressive on third down and in picking up first downs. He’s tied for 11th in the league with 12 receptions, including two for touchdowns, on third down, and 22 of his 33 receptions (67 percent) have gone for first downs.

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