Previously the longest-tenured Jets player, the 34-year-old agreed to a one-year deal with New England, pending a physical.
According to Monique Walker of the Boston Globe, Ellis rejected a contract offer from the Jets for one year at the veteran minimum of $910,000.
"The fact that he chose them. There's no way I'm going to wish him well," Jets coach Rex Ryan said after hearing the news. "There's no chance of that. I wish him to be healthy, but I don't want him to play that well."
In last season's playoff meeting between the two clubs, Ellis had arguably the most impactful game of his career, with two key sacks of Patriots quarterback Tom Brady.
Ellis wasn't the only defensive end the Pats signed over the weekend. New England also reached a deal with former Washington Redskins DE Andre Carter.
Shortly after the NFL Lockout ended, the Patriots traded for troubled and talented defensive anchor Albert Haynesworth and chatty receiver Chad Ochocinco.