The deal is worth a maximum value of $26.3 million, including $10.5 million guaranteed, a league source told ESPN NFL Insider Adam Schefter.
The 6-foot, 208-pound Lewis is a New Orleans native, playing high school football in the city at O. Perry Walker. Lewis visited with the Saints earlier this week.
"We are excited to be able to add a player of Keenan's ability to our defense," Saints general manager Mickey Loomis said in a statement. "He was a top free-agent target for us and I know that he is very excited to be able to come home to play football."
Lewis, 26, stepped up in his first season as a starter, leading the AFC with 23 passes broken up, and is considered a rising player at a coveted position.
"I'm very excited to be able to come back to my hometown," Lewis said. "Having grown up here, I understand the passion that the fans have for the Saints and I'm blessed to be able to have the chance to play in front of them here in the future.
"I had a great visit with the Saints and am thankful for the time I spent with the Pittsburgh Steelers and wish them continued success."
Information from AFC North blogger Jamison Hensley and The Associated Press was used in this report.