The 28-year-old Scott will make $27 million during the first three years of the contract, agent Harold Lewis told The Associated Press.
"These guys really pursued me hard," Scott said in a statement released by the team. "They picked me up from my house early in the morning and really let me know they care, they are serious and they are committed to winning."
"The opportunity to play under coach Ryan again was huge," Scott said. "I've made it no secret how big a role he has played in me taking the steps from being an undrafted rookie free agent to where I am today. I wanted to keep that chemistry going.
"It's been so successful that I didn't want to lose that magic."
Scott, Ryan and defensive coordinator Mike Pettine killed time while waiting for the deal to be completed by taking a trip to a mall near the Jets' training facility.
"We just looked around and things like that, and nobody recognized anybody," Ryan said with a laugh.
Guard Brandon Moore also agreed to return to New York for a $16 million, four-year deal, a person familiar with the terms said on condition of anonymity because the team hadn't announced the contract.
Jets general manager Mike Tannenbaum would only say they were "close to signing" Moore and fullback Tony Richardson, who helped pave the way for Thomas Jones to lead the AFC in rushing last season.
However, NFL Network's Adam Schefter reported that Richardson re-signed with the Jets.
"We added The Mad Backer today," Ryan said. "What you've seen him do and accomplish in Baltimore, I think is just the tip of the iceberg. ... He's called The Mad Backer because he basically hates the guys in the other color jerseys."
Scott was a major part of a Ravens defense that ranked No. 2 overall and helped Baltimore reach the AFC Championship Game against Pittsburgh. Scott was believed to be the Jets' No. 1 target this offseason, despite former teammates Ray Lewis and Terrell Suggs -- franchised by Baltimore -- also being free agents.
"I think he's going to be more effective with this Jets defense because we're going to have some flexibility with him and David that, quite honestly, we never really had with Ray," Ryan said. "That's not taking anything away from Ray, but Ray was always the MIKE backer and I think now we can switch Bart and David in and out and it's going to give some identification problems to offenses."
Despite signing Scott, the Jets wouldn't completely rule out also signing Lewis.
"We never thought we'd add Brett Favre last August, so right now we're going to take each day one at a time and look at opportunities," Tannenbaum said. "I would never rule out or rule in any player."
Scott originally signed with Baltimore as an undrafted free agent out of Southern Illinois in 2002. He saw significant playing time in his fourth season at middle linebacker when Lewis was injured, and played in the Pro Bowl the following season after he registered a career-high 9.5 sacks and two interceptions.
Scott had 82 tackles and 1.5 sacks last season for the Ravens.
The Jets are expected to be busy again this offseason in free agency, a year after they spent $140 million on bringing in high-profile players like Richardson, Alan Faneca, Calvin Pace, Damien Woody, and trading for Kris Jenkins and later Favre.
While New York probably won't spend as much this winter, the Jets have several needs after allowing wide receiver Laveranues Coles to become a free agent and cutting tight end Chris Baker, linebackers David Bowens and Brad Kassell and defensive back David Barrett.
The speedy and versatile Washington will be entering the final year of his deal, and likely would command a contract of no less than $6 million per year. Darren Sproles, whom Washington is often compared to because of their size, speed and game-changing abilities, was tendered a one-year, $6.62 million offer by San Diego as a non-exclusive franchise player.
Information from The Associated Press was used in this report