Defensive end Shaun Ellis is switching sides in one of the NFL’s most intense rivalries.

The two-time Pro Bowl selection signed with the New England Patriots today after 11 seasons with the New York Jets. The Patriots also signed another former first-round draft pick, free agent defensive end Andre Carter, who has played 10 seasons with the San Francisco 49ers and the Washington Redskins.

Ellis, 34, had become the longest-tenured player on the Jets since he was taken 12th overall with a pick that New York obtained as compensation for letting coach Bill Belichick sign with the Patriots. The Jets said this offseason that they wanted him back but offered only the veteran minimum of $910,000; they used their first two draft picks to bolster their defensive line, taking Temple defensive end Muhammad Wilkerson in the first round and Hampton nose tackle Kenrick Ellis two rounds later.

“I’m sad he went there,” Jets linebacker Bart Scott said today. “I think he deserved the opportunity to retire as a Jet. It’s one of those weird things. When you hear Shaun Ellis, you associate him with the green and white, but I wish him well and everything other than playing against us.”

Jets coach Rex Ryan wouldn’t go that far.

“The fact that he chose them and all that, like I said before, there’s no way I’m going to wish him well,” he said on Sunday. “There’s no chance of that. I wish him to be healthy, but I don’t want him to play that well. I know the way he is, too. He’s going to be revved up, ready to go and our guys will, too.”

Ellis’ decision to sign with New England is an odd twist in the rivalry that was largely spawned by Belichick’s decision even as he was being promoted in New York to quit as “H.C. of the N.Y.J” and instead take over the Patriots. The teams eventually settled on a package of draft picks, the best of which turned out to be Ellis.

Things also got spicy when New England was caught videotaping the Jets’ sideline signals; the Jets turned the Patriots in, and they were fined and forced to surrender another first-round draft choice.

More troublesome for the Patriots, though, is the fact that the Jets have beaten them four of the last six times they’ve played, including a 28-21 playoff victory in Foxborough, Mass., in January. Ellis sacked Tom Brady twice in that game.

“Certainly Shaun has played a lot of good football against us,” Belichick said. “He’s 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.”

Ellis has 72½ sacks, trailing only Mark Gastineau’s 107½ and Joe Klecko’s 77½ on the Jets’ all-time list; Ellis also holds the franchise record for most playoff games. He told The Associated Press last year that he hoped to play 15 years in the NFL and get 100 sacks.

But when Ellis asked for a contract extension last offseason, the Jets cited their policy of having older veterans play out their contracts.

“They talk good and then go do something else, but it’s all a business,” Ellis told the AP last season. “For me, I definitely want to be here. I love playing here and I love the fans, and love the whole idea of being a Jet. I really can’t picture myself playing for anybody else.”

Last offseason, he was mentioned as possible trade bait or that he might be cut.

“That was kind of like a slap in the face,” Ellis said then. “I’ve been here and I felt like I’ve put in a lot of work for this franchise. I went through all the growing pains, along with the fans. I think I’ve probably been the most loyal Jet. I go out and play hard for the Jets and for the fans, and I feel their pain because I’m going through it, too.”

Ellis made the Pro Bowl in 2003 and 2009, with his best seasons in 2003 and 2004 when he had 12½ and then 11.

Carter, the seventh overall pick in 2001, has recorded double-digit sack totals three times in his career, with a career-high 12½ in 2002 with the 49ers and 10.5 in 2007 and 11.0 in 2009 with the Redskins.

“Andre is a player I spent a lot of time with prior to him coming out in the draft,” Belichick said. “I think he’s another high-quality individual, very professional, works hard, very well-conditioned athlete. He’s had a lot of production throughout his career. … What we’ve seen him do the first nine years of his career, that we could use his ability on the edge.”

Also today, the Patriots re-signed defensive lineman Gerard Warren.