Ian Rapoport of NFL Network reported the news.
Williams, a 2016 fifth-round pick, was released by the Buffalo Bills in September before signing with Denver's practice squad. He rushed for 94 yards and a touchdown as a rookie.
The Saints currently rank third in rushing with 142.2 yards per game. The one-two punch of Mark Ingram and Alvin Kamara has emerged as one of the NFL's best and been particularly stellar since the Saints traded Adrian Peterson to the Arizona Cardinals.
Williams' signing is unlikely to have any impact on the distribution of carries moving forward. Third-stringer Daniel Lasco suffered a season-ending neck injury in Sunday's win over the Buffalo Bills. He will require surgery to repair a bulging disk.
"The prognosis is good. We're fortunate that it wasn't more severe," Saints coach Sean Payton told reporters. "I know his teammates and coaches all felt relieved that he was able to come back on the plane with us."
There was a bidding war among teams for Williams' services when he hit the open market. His deal with Denver called for him to make $30,000 per week on the practice squad.
No terms of his deal with New Orleans have been released.