The men who inflicted defeats on former pound-for-pound king Manny Pacquiao in his last two fights will now face each other in October.
Marquez is aiming to become the first Mexican to win world titles at five different weight divisions, while Bradley wants to cement his reputation as one of the best fighters around, and both men know how hard the fight will be.
"It will be an honour to step in the ring with Marquez," said Bradley. "I am looking forward to displaying my skills and giving the fans a competitive fight.
"I know one thing that he and I will have in common, stepping into that ring, is that we're both warriors."
Marquez echoed the sentiments.
"This is a very tough fight. I am facing an undefeated fighter who has something that I want very much," he said.
"Bradley is one of the best pound for pound fighters in the world. I think we have the styles to make a great fight."
The fight will take place in Las Vegas on October 12.