Ellis and the Patriots reached agreement on a one-year deal, a league source told ESPN NFL Insider Adam Schefter. Ellis will receive $4 million this season with a chance to make another $1 million in performance incentives, a source told ESPN.com senior NFL writer John Clayton.
Terms of Carter's deal were not disclosed.
The defensive line won't be completely new, however, as coach Bill Belichick announced the team also has re-signed Gerard Warren.
"With Gerard, it's something we agreed to do earlier, and today happened to be the day for it," he said.
Warren spent the 2010 season with the Patriots, elevating into a starting role at left end when veteran Ty Warren was lost for the season in August with a hip injury.
The Patriots have been looking to upgrade their pass rush. In 10 seasons split between the 49ers and Redskins, Carter has 66 sacks. He had only 2½ last season but 11 in 2009.
Ellis has piled up 72½ sacks, ranking third on the Jets' career list behind Joe Klecko (77½) and Mark Gastineau (107½).
"Certainly Shaun has played a lot of good football against us," Belichick said. "Been a very productive player. Durable. Very consistent. It seems like every time we play him, he lines up there and we have a hard time with him. I'm glad we had an opportunity to add him to our team. I think he brings a really good presence in terms of his leadership and professionalism, as well as experience, and his style of play and performance."
Ellis admitted Monday that the lack of interest from the Jets after 11 seasons there left a bitter taste in his mouth.
"If you look at it that way, from an emotional standpoint, yeah," said Ellis, who wore shorts and T-shirts during New England's afternoon session and spent time with the strength and conditioning staff. "But you have to look at is as a business as well. (The Jets) had a choice of going after the guys that they feel like they need, or the guys they want to try to surround their team around. I just wasn't in their plan. Like I said, I'm a Patriot now, I'm part of this family. I'm going to go out there and play my best."
Asked about Ellis' decision to sign with New England, Jets coach Rex Ryan said Sunday: "The fact that he chose them, and all that, I think (I) said before, there's no way I'm going to wish him well. There's no chance of that. I wish him to be healthy, but I don't want him to play that well."
Word clearly got back to Ellis, who offered nothing but fondness when referencing his time in New York.
"It's Rex. I like to say I wish him well, and wish him all the success, so that's how it is," said Ellis. Pressed to say whether he really felt that way, he said: "Yes, I do. I have a lot of respect for the guy. Obviously, I feel like it's not mutual, but I respect him."
The Patriots had looked thin at defensive end in training camp, with Jermaine Cunningham (second year) and Eric Moore (sixth year) running with the top group as part of a four-man line. There was a significant drop-off in experience after Cunningham and Moore, which the Patriots addressed, in part, with the signing of speed rusher Mark Anderson (6-foot-4, 255 pounds) on Friday.
At 6-foot-5, 290 pounds, Ellis is more stout than the team's current ends from a run-game perspective, but also has shown the ability to generate a pass-rush. Ellis has played in both 3-4 and 4-3 schemes in his time with the Jets.
Now he has to adjust to playing on the other side of the rivalry.
"It's a team that always was on top of our division -- they still are today," Ellis said of the Patriots. "Trying to catch them for 11 years, of course you feel something, a little kind of hatred towards the Patriots over those 11 years. I understand. They know what it takes to be a champion and they've been doing it. I've wanted to feel that feeling for however long, so hopefully that time will come."
At 6-4 and 255 pounds, Carter has had triple digits in sacks three times with a career high 12½ in 2002.
"I think he's another high-quality individual, very professional, works hard, very well-conditioned athlete," Belichick said. "
He's had a lot of production throughout his career. Last year when Washington went to the 3-4 defense, it kind of wasn't a good fit for him in that system. But we feel like what we'll ask him to do this year, relative to what he was asked to do last year, and what we've seen him do the first nine years of his career, that we could use his ability on the edge."
Belichick says he also sees Anderson as "an edge player, as a player on the perimeter of the defense, absolutely. But how much, or when that is, I don't know."
After adding four defensive linemen to the team since last Friday, the Patriots have 21 defensive lineman in camp -- the most Belichick has had -- and are now at the 90-man limit.
The Patriots also released defensive back Brandon McGowan on Monday. He missed all of the 2010 season with a chest injury after starting 11 games in 2009.
ESPN NFL Insider Adam Schefter, ESPN.com senior NFL writer John Clayton and ESPNBoston.com's Mike Reiss and Chris Forsberg contributed to this report. Information from The Associated Press also was used.