The deal will be for two years and $5 million, per Pro Football Talk. It also reportedly includes up to $1.5 million in incentives for sacks.
The Saints previously hosted Edwards for a visit on Wednesday night.
Edwards, 25, is a former second-round pick of the Raiders back in 2015. He was entering the final year of his four-year, $6.017 million rookie contract when the Raiders cut him loose during the 2018 preseason.
He was quickly claimed off of waivers by the Giants in September and played out the year in New York.
In 2018, Edwards appeared in 15 games for the Giants and recorded 14 total tackles, three tackles for loss, two sacks, and one forced fumble.
We have him featured in our Top 100 Available Free Agents list.