Khan had called for a rematch after complaining about several aspects of their original bout in Peterson's home city of Washington DC in December.
The pair will meet for a second time at the Mandalay Bay Hotel on May 19 when Peterson will put the WBA and IBF super lightweight world titles on the line.
Peterson was reported to have other options but has agreed to fight Khan again.
Peterson said: "I feel really good about my decision.
"I went over every option available to me in terms of the fights that were on the table. I weighed each one of them looking at the pros and the cons and at the end of the day this is the one that made the most sense all the way across the board.
"It's at a neutral site and, when I beat him this time, he won't have anything to complain about."
Khan had highlighted several grievances about the original contest, chiefly referee Joseph Cooper's deduction of two points, the judges' scoring of the bout and the unexplained presence of 'mystery man' Mustafa Ameen at ringside.
With a date set for the rematch Khan has one thing on his mind.
He said: "I'm delighted that I have finally been given the chance to avenge the result of my last fight.
"It's clear I wasn't happy with what went on in the previous fight, but that takes nothing away from how Lamont Peterson fought.
"I'm going to take care of business inside the ring and this fight is going to be just as exciting as the last one. The only difference is going to be in the outcome."