Amir Khan returned to boxing last April after 23 months away from the sport and secured two wins in 2018.
The Briton had an offer to face domestic rival Kell Brook in a bout, which his team had said would prove more financially rewarding.
But he will instead be a heavy underdog against 31-year-old Crawford, who has held world titles in three divisions.
A news conference is due to take place early next week to outline a venue, either in New York or Las Vegas. Both are cities in which khan has boxed before - this time, though, he will go up against an American widely regarded as one of the sport's best pound-for-pound fighters.