Okafor said Tuesday the Saints plan to use him at defensive end.
"Obviously they're making defense a big priority this offseason. And there's an opportunity at the opposite D-end away from Cam (Jordan), and I know I can be that guy. I saw that there was the opportunity, and I pounced on it.
"I think the Saints are so close to being contenders this year, and for me to be able to come in and contribute right away and make something special happen here, I couldn't turn that down."
Coach Sean Payton said before free agency that it was a must for the Saints to add an edge-rushing defensive end, but many of the elite pass-rushers were kept off the market via the franchise tag.
Okafor is not a bad consolation prize, however.
He is a solid role player who can spell the team's edge rushers while still pressuring offenses. He is long and lean and has shown the ability to get to the quarterback, with 13.5 career sacks, including 3.5 in 2016.
Okafor, who turned 26 in February, was drafted in the fourth round (No. 103 overall) by the Cardinals in the 2013 draft.
The Saints' defense showed signs of improvement in Dennis Allen's first full season as coordinator in 2016, but they still ranked 27th in the NFL in yards allowed and 31st in points allowed while New Orleans finished 7-9 for the third consecutive year.
ESPN's Josh Weinfuss contributed to this report.