Promoter Frank Warren announced on Tuesday that Burns would defend his WBO lightweight title against the Londoner in Glasgow on September 22.
Talks have been ongoing over setting up the clash since Burns stepped up to lightweight in impressive style with a convincing victory over Australian Michael Katsidis, who had previously beaten Mitchell emphatically at Upton Park.
Former world super-featherweight champion Burns, who defended his lightweight title against Paulus Moses in March, said: "The fight's been on the boil for the last couple of years and the fans and press have been desperate for it to happen, it's fantastic that it's on at last.
"We are both at the top of our game now and I'm in this sport to prove that I'm the best, next to me Mitchell's the best around and it will be great fight between two warriors.
"He put on a great showing against John Murray last year that showed just how good a boxer he is to take apart another champion.
"But this fight is the fight I've wanted and it's got me really excited, Mitchell's going to bring out the best in me and I believe that the fans are going to be in for an unbelievable fight."
Mitchell's eight-round victory over Murray in July last year, on the undercard of Burns' victory over Nicky Cook, was voted British fight of the year.
Mitchell, whose loss to Katsidis is his only professional defeat, said: "I'm promising you now you're going to see the best fight of the year or any year.
"This is a real fight between the two best in the division and it's not going to be for the faint-hearted.
"I rate Burns very highly, he's a great fighter and has really proved himself as one of the top champions in the world.
"I'm going into the lion's den and I know I can beat him and take the world title.
"Burns is a top kid and I've got to be at top of my game, the fittest and strongest I've ever been in my life to win."
The venue for the fight has yet to be decided. Burns last fought at a packed Braehead Arena but the Coatbridge boxer has been keen to stage an open-air fight in a football stadium.