The Jets chose a familiar face as their new head coach.

Gang Green agreed to a deal with former Dolphins coach Adam Gase on Wednesday, according to a source, to become the 17th coach in Jets history.

Gase spent the previous three seasons with the Dolphins, leading them to the playoffs in his first year, but getting fired after two losing seasons.

The hiring of Gase brings an end to a coaching search that had some twists and turns over 10 days. After firing Todd Bowles on Dec. 30 after the season finale in New England, Jets CEO Christopher Johnson and general manager Mike Maccagnan began looking for a new leader for their franchise.

The 40-year-old Gase was one of eight candidates known to have interviewed for the job. The other top candidates were Buccaneers offensive coordinator Todd Monken and Baylor coach Matt Rhule.

The expectation is that Gase will bring his offensive coordinator from Miami, Dowell Loggains, with him to the Jets. A source said former Broncos coach Vance Joseph is a candidate for the defensive coordinator job, but Joseph is still a candidate for the Bengals’ head-coaching opening. Joseph worked with Gase in Miami in 2016.

The Jets sat down with Gase last Friday and were impressed by him. They liked his history of working with quarterbacks, his background as an offensive coach and the fact he had previous head-coaching experience. Gase, who went 5-1 against the Jets as Dolphins coach, is the first coach the franchise has hired with previous NFL head-coaching experience since 1997 when they hired Bill Parcells. He is the first head coach hired from the offensive side of the ball since Rich Kotite in 1995.

The Dolphins fired Gase on Dec. 31 after he went 23-25 in three seasons in South Florida. Miami went 7-9 in 2018, ending the year on a three-game losing streak. That was enough for owner Stephen Ross to send Gase packing.

The Jets considered Rhule a strong candidate, but his lack of NFL experience worked against him. There were concerns about how he would put together a coaching staff.

The Jets wanted a head coach who would work well paired with quarterback Sam Darnold, coming off a promising rookie season, and felt Gase fit the bill. Gase’s reputation took a bit of a hit in Miami, but he did make the playoffs in 2016 with a healthy Ryan Tannehill. After that, Tannehill struggled to stay on the field and Gase could not win big with Jay Cutler in 2017 or with Brock Osweiler in 2018.

Still, Gase has a reputation around the league as being good with quarterbacks. He was a hot name in 2016 when the Dolphins hired him. During this job cycle, he also received interviews with the Cardinals and Packers.

The Michigan native got to know Nick Saban as a student at Michigan State and then followed him to LSU to get his start as a graduate assistant. After some entry-level jobs with the Lions, Detroit offensive coordinator Mike Martz promoted him to quarterbacks coach in 2007.

“He is very, very bright,” Martz, the former Rams head coach, told The Post last week. “He has terrific leadership. I think he’s mature beyond his years. I think he has a very engaging personality. I give him high marks in everything.”

After Detroit, he spent a year with the 49ers before joining the Broncos in 2009 as their wide receivers coach. He became the quarterbacks coach in 2011 and worked with Tim Tebow during his magical playoff run in Denver. He was promoted to offensive coordinator in 2013 and spent two years running a record-setting offense with Peyton Manning at quarterback.

Gase spent a year with the Bears working with Jay Cutler before the Dolphins hired him.

He is known as a confident person who won’t pull any punches, which rubs some people the wrong way. He reportedly clashed with Ross, the Dolphins owner. With Miami, he had control over personnel, which he won’t have with the Jets. Johnson made it clear Maccagnan will retain control over the roster. It does not appear that was an issue for Gase.

Many of his issues with the Dolphins seemed to center around his personnel decisions, rather than his coaching.

“I don’t know what happened in Miami,” Martz said. “I know he had some injuries and that’s tough. I’ve been through that myself. I don’t think any of that is an indictment on him nor the organization. It’s just kind of luck more than anything else.”

The Jets also interviewed former Packers coach Mike McCarthy for the opening, but sources said he was not a strong candidate for the job.

Along with Rhule, Monken and McCarthy, the Jets also interviewed Chiefs offensive coordinator Eric Bieniemy, Cowboys defensive backs coach Kris Richard, former Lions and Colts coach Jim Caldwell and former Texas Tech coach Kliff Kingsbury, who took the Cardinals job on Tuesday.