The contract is worth the veteran minimum of $2.4 million, a source told ESPN's Marc J. Spears.
"Fit is first and foremost when I'm thinking about where I'll play next," Crawford said in August, according to the Seattle Times' Percy Allen. "Last year, I may have made the mistake of not thinking fit all the way through."
Crawford supplies Phoenix with playmaking and perimeter depth, as the Suns will enter the year sans Devin Booker due to injury.
The three-time Sixth Man of the Year averaged 10.3 points through 80 contests last season.