The Pelicans said they will keep the guard for the remaining 14 games of their season.
The second year of the contract has a guaranteed date for 2017-18, according to The Vertical, which earlier reported Crawford's pending deal.
Crawford said he heard often since his last game with the Golden State Warriors in 2014 that he should be back in the NBA, including from his grandmother, who he joked thought Crawford was being "blackballed."
On Thursday, his father was able to call her with some good news.
"She's been on me hard," Crawford said. "I'm happy she got to see this."
The 28-year-old shined after signing a 10-day contract on March 6, averaging 14.2 points on 51 percent shooting and 3.2 assists off the bench in five games.
He then played in China and the D-League, most recently for the Grand Rapids Drive.
Crawford said Friday that his time outside the NBA helped him appreciate the little things in life and grow on a personal level.
"This journey that I'm on -- it's a basketball journey because that's the business, but it's really life," he said. "I learned a lot of life lessons [while] becoming a man. Learning things that's small and things that are big, things that are thrown at you that you can't control how to deal with them. Just took it as a man."