Greer was injured on a play in which he leaped to break up a pass intended for Jon Baldwin in the first half of New Orleans' victory over San Francisco on Sunday. His knee buckled and appeared hyper-extended when he landed, and he was carted to the locker room.
Payton had hinted Monday that the injury was serious, but waited until Tuesday to disclose the ACL tear and report the roster move.
New Orleans also has signed defensive back Trevin Wade, who was drafted by Cleveland and played much of last season, but had been a free agent throughout this season.
Wade was signed to add depth. Payton said second-year cornerback Corey White is expected to take over Greer's starting role, as he did during last Sunday's game, in which he had an interception.
"He's been consistent this season," Payton said of the 6-foot-1, 205-pound White. "He's been a very good tackler. He has good size and length. He's strong and very quickly got adjusted to a lot of the snaps that he had outside. I think he has good football instincts as well and I think that serves him well on game day."
Defensive coordinator Rob Ryan said White has "really been an ascending player."
"He has been outstanding. He is a physical player. He is a smart kid. He is getting better and better," Ryan said. "We've lost some great players along the way and we are so fortunate to have excellent players behind him and that is what this Corey White has been doing, begging for an opportunity. He is going to be great when he gets in there."
White said he was sorry about the circumstances that led to his central role on the defense, but sounded optimistic that he was ready for it.
"It's unfortunate that Jabari went down like that with him being a good leader on and off the field for us. That's tough," White said. "But we always believe in all our teammates here and we believe in the 'next man up.' I'm pretty sure Jabari believes in me and so does every one of my secondary teammates, so we'll see how it goes."
As much as Ryan raved about White, he did not diminish the loss of Greer, a popular 10-year veteran who was part of the Saints' Super Bowl team.
"He is a great person. We will miss him in the locker room most. But he was having a great year," Ryan said. "He was doing everything we asked him to do and then some."
Payton said the Saints signed Wade because they thought he handled nickel back responsibilities well in Cleveland last season and because he had a good workout in New Orleans.
"He's someone that has decent speed but very good feet," Payton said. "We'll see how he gets up to speed with what we're doing. That will take a little bit."
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