The deal is for $3 million and includes incentives that could raise its value to $5 million, a source told ESPN NFL Insider Adam Schefter.
Fairley took to Twitter on Monday to thank the Rams and express his excitement at playing in New Orleans.
Thanks to the Rams organization for a great year...#whodat Saints nation let's get it ⚜⚜⚜— Nick Fairley (@Nick_Fairley251) March 28, 2016
Fairley came to the Rams on a one-year deal in 2015 in hopes that he would play well enough to land a big-money, long-term contract.
The 28-year-old Fairley is a disruptive 3-technique tackle, one of two positions that Saints coach Sean Payton listed as a "must" last week during the NFL owners meetings. The Saints used veteran Kevin Williams as their starter in the 3-technique role last year, but he remains unsigned this offseason.
The New Orleans defense ranked last in the NFL last season in points allowed and 31st in yards allowed. It set NFL records for most touchdown passes allowed in a season and highest opponents' passer rating. The Saints have added former Rams middle linebacker James Laurinaitis in free agency to become the "quarterback" of their defense.
They will have to clear out salary-cap space to fit in Fairley's new deal, since the franchise had less tham $300,000 in cap room to start the week.
Fairley drew interest from a handful of teams, including the New England Patriots.
Last year, Fairley worked as the primary backup to Aaron Donald and Michael Brockers, getting most of his opportunities on third down. He finished with 29 tackles, a half-sack and a fumble recovery in 15 games.
Fairley was a first-round pick of the Detroit Lions in the 2011 NFL draft. He had 13.5 sacks in four seasons in Detroit.
ESPN Saints reporter Mike Triplett and Rams reporter Nick Wagoner contributed to this report.