The New York Jets are finalizing a contract with former Cleveland Browns interim coach Gregg Williams to be their defensive coordinator, a source told ESPN's Adam Schefter on Tuesday.

Williams becomes the first big hire for new head coach Adam Gase, who was formally introduced on Monday. The Jets targeted Williams at the start of their head-coaching search but Gase was on board with the hiring, Schefter reported.

Williams, 60, became available when he wasn't re-hired by the Browns, despite a 5-3 record after replacing Hue Jackson at midseason.

The Gase-Williams pairing should be fascinating because they've never worked together, and they're both considered headstrong personalities.

"I probably need to spend my time with the quarterback," Gase said Monday. "That's why, whoever we bring in here on defense has to do a great job of making sure he's really the head coach of the defense."

Williams' arrival likely means a radical change for the Jets, who have operated a 3-4 base defense since 2006. Williams typically runs an attacking 4-3 scheme, predicated on heavy blitzing. He inherits a unit that finished 29th in total yards and 23rd in scoring. In fact, the Jets allowed 441 points, the second-highest total in franchise history.

The top player was safety Jamal Adams, who made the Pro Bowl in his second season. The Jets believe Williams' aggressive scheme and fiery personality will spark defensive end Leonard Williams and linebacker Darron Lee, former first-round picks who haven't lived up to expectations.

With the third pick in the draft, the Jets are in position to select a top defensive lineman or perhaps a much-needed edge rusher.

Williams ran the Cleveland defense for two seasons, achieving mixed results. The Browns finished 30th in total yards, but they reduced their point total for the second straight year, ranking 21st in scoring defense (392 points).

His hallmark is creating turnovers, an area where the Jets need a lot of improvement. They had only 20 takeaways -- 11 behind the Browns, who finished second to the Chicago Bears.

Williams has bounced around the league since 1997, working as a defensive coordinator for seven different teams. He was the New Orleans Saints' coordinator from 2009 to 2011 and was implicated in the Bountygate scandal, which resulted in a one-year league suspension.

He was the Buffalo Bills' coach from 2001 to 2003, compiling a 17-31 record.