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

The two-time Pro Bowl selection officially signed with the New England Patriots on Monday 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 Bill Belichick become coach of the Patriots.

“It’s the same; I’m just on the other side now,” Ellis told reporters in Foxborough, Mass., after the Patriots practiced. “It feels like home. It feels like a place that’s all about winning, like they have been. I’m just happy to be a part of it.”

The Jets had said that they wanted Ellis back, but they offered only the veteran minimum of $910,000 and, Ellis said, refused to increase it substantially when he went back to them for a final offer. 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.

“It’s the nature of this sport. I accepted it and found a new home,” Ellis said. “I just wasn’t in their plan. … I’m a Patriot now. I’m part of this plan.”

Jets linebacker Bart Scott said he was sad to see Ellis switch sides.

“I think he deserved the opportunity to retire as a Jet,” Scott said at Jets training camp in Florham Park, N.J. “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. So, it’ll be fun, going against him but, obviously, I’ve got a great deal of respect for Shaun.”

Ellis’ decision to sign with New England is an odd twist in a 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 past six times they’ve played.

“Of course you built up a little kind of hatred toward the Patriots over the 11 years,” Ellis said. “I understand what it takes to be champion, and they’ve been doing it. And I have been wanting to feel that feeling for however long. So, hopefully the time has come.”

In their most recent meeting, the Jets beat the Patriots 28-21 in Foxborough in January to advance to the AFC championship game. Ellis had five tackles and sacked Tom Brady twice.

“Certainly, Shaun has played a lot of good football against us,” Belichick said. “He’s been a very productive player – he’s durable and very consistent. It seems like every time we play him, he lines up there and we have a hard time with him. The fact that we had an opportunity to add him to our team, we feel fortunate.”

Ellis made the Pro Bowl in 2003 and 2009, with his best seasons in 2003 and 2004 when he had 12 and then 11½ sacks. He has 72½ sacks in his career, 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.

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

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 10½ in 2007 and 11 in 2009 with the Redskins.

“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. … What we’ve seen him do the first nine years of his career, that we could use his ability on the edge.”

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