FOXBOROUGH, Mass. – Randy Moss and Corey Dillon were malcontents when they joined the New England Patriots. Rodney Harrison arrived with a reputation as a dirty, washed-up player.

All of them fit in very well with their new team.

Now Albert Haynesworth and Chad Ochocinco are coming and “The Patriot Way” will be tested once again.

After Haynesworth’s seasonlong feud with Washington Coach Mike Shanahan, the 335-pound defensive tackle was traded by the Redskins on Thursday for a fifth-round draft choice in 2013.

Ochocinco almost certainly will test Patriots Coach Bill Belichick. The Patriots are closely monitored by Belichick, who tries to control his players’ public comments.

The deals were confirmed by people familiar with them speaking on condition of anonymity because the teams had not announced them.

The Patriots agreed to a new three-year contract with Ochocinco, but it was not known what the Bengals received in return.

The relationship between Belichick and Ochocinco, with extremely different public personas, is unexpectedly warm.

“I like Chad,” Belichick said before last year’s season opener between the teams. “I like him as a player. I like him as a person. I like his enthusiasm and the fun he has with football, and I like how he competes on the football field. I have a lot of respect for that.

“An odd couple, but in the end I think we have a lot of things in common.”

They grew closer during Pro Bowl practices.

“It became a relationship beyond just a football player and a coach,” Ochocinco said. “He became a friend of mine. He has a lot of respect for me in my game and I have a lot of respect for him in everything he’s done as a coach.

“We just became really close and fond of each other’s work. He’s one that I look up to tremendously, one that I’ve never played for, but I show the same respect as if he was my own head coach.”

Now Belichick is his coach.

Ochocinco, who caught 12 passes for 159 yards and a touchdown in a 38-24 Patriots win last year, provides another option for Tom Brady, who has been without a deep target since the Patriots traded Randy Moss to the Minnesota Vikings after four games last season. In 10 seasons, all with the Bengals, Ochocinco has 751 catches for 10,783 yards and 66 touchdowns.

But when the Bengals drafted wide receiver A.J. Green in the first round in April, it became likely that Ochocinco would be released, traded or told to take a large pay cut.

Some of Haynesworth’s new teammates said there’s reason to think his problems with authority will clear up in New England.

Two defensive linemen who could be starting alongside Haynesworth in the 3-4 defense — the alignment that helped fuel Haynesworth’s discontent with Shanahan after signing a $100 million, seven-year contract in 2009 — think he’ll adjust to the players’ unselfish approach.

“You can see that Albert wasn’t really happy in his situation,” end Ty Warren said, but “all you see is what goes on (from) the outside and sometimes that’s only half of the truth. So, I don’t think it’s going to be a problem, with the structure of this locker room, the guys that’s in this locker room.”

Vince Wilfork, primarily a nose tackle, saw the most action at defensive end of his seven-year career last season. Playing next to Haynesworth, the 325-pound Wilfork likely would spend even more time on the outside if that’s what Belichick wants.

“It’s always team first. That’s ‘The Patriot Way.’ If you can’t put the team first you won’t be here,” Wilfork said.

“We had guys come through here with a rap sheet and (people) say, ‘he can’t be handled.’ ‘This guy can’t do this,’ and you know what, it worked out fine for us. So, I don’t think it will be a big problem.”

Moss, eager to leave the Oakland Raiders, didn’t go all out in 2006 and was traded to the Patriots. He caught 98 passes with an NFL-record 23 touchdown catches in 2007 and didn’t cause trouble until last season, when he was traded.

Dillon, who complained about being stuck with a consistently bad Bengals team, was picked up in March 2004 after being cut and was a major contributor that year to the Patriots’ championship.