The British boxer lost his WBA and IBF light-welterweight titles to the American last month, but the defeat was marred by controversy surrounding the referee and a 'mystery man', later identified as Mustafa Ameen, appearing to handle the scorecards.
"The WBA ordered an immediate rematch," Golden Boy Promotions' Richard Schaefer told ESPN. "I'm thrilled that he's getting one and hope we can start the negotiations and get the fight done.
"Amir and Lamont are both terrific young men and athletes who fought their hearts out in Washington in December and I'm sure this decision will get applause by fight fans around the world.
"The rematch will be one of the most anticipated fights of 2012 because both guys are exciting, young and I think it's exactly the kind of fight people want to see."
The date for the encounter has yet to be decided.