Jenkins was expected to join a playoff-bound team and will do so with the Saints, who enter Monday night's game against the Colts at 10-3 and in first place in the NFC South.
The Saints are taking a bit of a risk by adding a strong personality such as Jenkins with two weeks remaining in the regular season. But they are banking on getting him at his most motivated.
Although Jenkins has battled some inconsistency, he has been a standout player for much of his eight-year career, starting 111 career games and making the Pro Bowl in 2016.
The Saints will owe Jenkins two weeks of salary at $597,000 per week -- just under $1.2 million for the remainder of this season, along with a 2020 contract that is scheduled to pay him $11.25 million.
The Giants waived Jenkins Friday, two days after he made an inappropriate remark to a fan on Twitter. Jenkins called a critical fan a "retard" when taking exception to questioning about why the stats Jenkins was using to showcase his effectiveness weren't contributing to victories.
Jenkins, 31, said Thursday that the usage of the word was "slang" that is "just part of my culture."
Giants coach Pat Shurmur met with Jenkins on Wednesday and said in a statement Friday that Jenkins' refusal to admit that what he did was wrong led to his release.
This is now the second straight year the Saints have added a cornerback from the Giants in the middle of the season after they traded fourth- and seventh-round picks for Eli Apple last year. And now Jenkins and Apple could wind up competing for the Saints' No. 2 cornerback job alongside Marshon Lattimore.
Jenkins started all 13 games for the Giants before his release -- primarily as an outside corner. The 5-foot-10, 190-pounder did move inside to the slot last week, however, and played well in that role. So the Saints could also consider using him inside.
Apple, who is scheduled to be a free agent after this season, has played well for much of his tenure in New Orleans. However, he has struggled over the last two weeks against Atlanta and San Francisco. The Saints allowed 354 passing yards in their 48-46 loss to the 49ers last week, the most they had allowed since a Week 3 win at Seattle.
New Orleans' defense has taken several significant hits due to injury in the past week. Defensive tackle Sheldon Rankins and defensive end Marcus Davenport were placed on injured reserve. And in the secondary, safety Vonn Bell and cornerbacks Patrick Robinson and Johnson Bademosi were previously ruled out for Monday night's game.
Since New Orleans has yet to play its Week 15 game, the Jenkins claim won't be made official until Tuesday.