Alex Smith retired Monday after making an improbable comeback from a gruesome broken leg, saying he’s ready to leave the NFL but believing he’s still able to play quarterback.

Smith made the announcement on Instagram a few weeks shy of his 37th birthday, hoping to enjoy more time with his family.

“I want to say thank you for believing in me, and thank you for helping me believe in myself — and in the impossible,” Smith said. “Because even though I’ve got plenty of snaps left in me, after 16 years of giving this game everything I’ve got, I can’t wait to see what else is possible.”

Smith earned AP comeback player of the year honors for getting back on the field last season, two years removed from an injury that required 17 operations. After breaking his right tibia and fibula in a game Nov. 18, 2018, against the Texans, he said he wondered if he’d be able to take walks with his wife or play with his kids in the yard — let alone play in the NFL again.

He was hospitalized for almost a month and survived a life-threatening infection in addition to the operations. Smith spent the next year and a half rehabbing and was back at practice when Washington assembled for training camp last summer.

Smith’s first game action since the injury came Oct. 11 when Kyle Allen was injured, and he made his first start on the road against the Lions on Nov. 15. He went 5-1 as the starter, including a road victory over the Eagles in Week 17 on a strained right calf that clinched the NFC East title for Washington.

“He accomplished the greatest comeback in professional sports history and was a huge part of our team’s success this past season,” owners Dan and Tanya Snyder said in a statement.

“We witnessed every step of Alex’s comeback, and he personifies perseverance, strength and the will to never give up.”

The injury prevented Smith from playing against the Buccaneers in the wild-card round the next week, which Taylor Heinicke started and impressed enough to earn another contract.

Smith told GQ earlier this year that the organization didn’t expect him to play again.

Coach Ron Rivera agreed with those comments, noting he was worried about Smith’s health.

“The biggest thing he and I talked about, really, was that there was really no roadmap to get us to where we were,” Rivera said last month. “He worked his butt off to put himself in a position to come back and play. ... It was always in the back of my head: ‘What if he gets hurt again? What if he hurts that leg, that specific leg?’ I don’t want to be the guy that put him back on the field to let him get hurt again.”

Washington released Smith in March and signed veteran quarterback Ryan Fitzpatrick. Smith initially expressed his intent to keep playing but went unsigned more than a month into free agency.

“I’m going to take a little time to enjoy a few of those walks with my wife, and my kids have no idea what’s coming for them in the backyard,” he said.

A self-professed “skinny, no-name recruit,” Smith was the No. 1 overall pick in 2005 and played 14 seasons for the 49ers, Chiefs and Washington. He threw for 35,650 yards and 199 touchdowns in 174 regular-season games and played in seven playoff games.

Super Bowl winner and 2018 MVP Patrick Mahomes of the Chiefs said Smith “really helped me be the quarterback I am today.”

Chiefs coach Andy Reid called Smith one of his all-time favorite players.

“Football wouldn’t let me give up because, no, this isn’t just a game,” Smith said. “It’s about how hard and how far you can push yourself.

“It’s about the bond between those 53 guys in the locker room and everybody else in the organization.

“It’s about fully committing yourself to something bigger.”

AP writer Dave Skretta contributed.