The Cleveland Browns have another new quarterback, with former Eastern Michigan star Brogan Roback signing a free-agent contract Thursday.

He has agreed to a three-year deal, and becomes the fourth quarterback on the current Browns roster, including last month’s No. 1 overall pick, Baker Mayfield, as well as expected starter Tyrod Taylor and former Michigan State standout and veteran NFL backup Drew Stanton.

“It’s absolutely motivating,” Roback told The News, speaking of the quarterbacks he will be competing against. “You better bring it every day because you know those guys will. They’re big-name guys.

“It’s gonna be good just to be around them — and not only motivating, but also a wonderful opportunity at the same time. These guys are great players for a reason.”

Roback signed his first professional contract after attending a mini-camp workout last week with the Baltimore Ravens.

He was supposed to fly out for a workout with the Tampa Bay Buccaneers this weekend, but those plans are scrapped.

He reports to the Browns on Sunday, and will take his physical Monday.

“I’m going to do everything I can to make sure they made the right decision,” Roback said.

Roback, 23, goes down as one of the most accomplished quarterbacks in Eastern history, even if he didn’t get picked up in April’s NFL Draft — he was vying to become the second Eastern quarterback ever to be drafted, after the Lions took Charlie Batch in the second round in 1998.

There was some pre-draft buzz he could be a sleeper pick, but it never materialized, which Roback acknowledged was disappointing.

“There’s a feeling that you get when you sit there and you wonder, and you don’t know what’s next,” he said. “That’s a feeling I’m not going to forget. That’s a feeling I’m carrying with me and always will. That’s the motivation.”

Despite plenty of adversity during his collegiate career — Roback lost his starting job after new coach Chris Creighton was hired, and he was suspended early in his redshirt junior season — the Toledo, Ohio, native owns Eastern records in touchdown passes (57) and yards of total offense (8,876), and is second in completions (745) and passing yards (8,653). Two years ago, despite the early season suspension, he led the Eagles to their first winning season since 1995 and their first bowl game since 1987.

In last season’s finale, he suffered a fractured fibula that kept him from participating in the NFL Combine. He did later get workouts with several NFL teams, including the Pittsburgh Steelers and Detroit Lions.

“It’s a little detour route,” said Roback, who has good size for a pro quarterback — at 6-foot-3 and 206 pounds — as well as excellent arm strength and above-average mobility. “Obviously, things didn’t go the way I anticipated, but that’s kind of how my story’s been.

“I’m more than grateful for the Browns organization for taking this risk.

“This is a new chapter. This is where the real work starts.”

The Browns play the Lions in the final preseason game for both teams, on Thursday, Aug. 30, at Detroit at 7 p.m.