The 22-year-old heavyweight had been hoping to face Dereck Chisora for the British belt, but he has now agreed to fight Rahman on the undercard of the Amir Khan-Paul McCloskey clash on 16 April, live on Sky Box Office HD.
Rahman is best known for his dramatic upset win over Lennox Lewis back in 2001 when he dethroned the British champion with a huge right hand in the fifth round of their title fight in South Africa.
The American would later reclaim the WBC belt in 2005, but his most recent step up to world title level ended in failure when he was halted by Wladimir Klitschko in 2008.
Rahman has since racked up four wins by knockout and he has only lost to world class opponents during a career which has spanned 59 fights.
Lewis crushed 'The Rock' in a rematch and the 38-year-old was also beaten by world champions John Ruiz and Oleg Maskaev, while David Tua is the only man to have beaten him who did not claim a top title.
Fury is yet to suffer defeat in his fledgling career and will be keen to send out a message to his rivals with a dominant win over the big-hitting Baltimore man.
Respected trainer Emanuel Steward has worked with Fury this year and he impressed while halting Brazilian Marcelo Luiz Nascimento in his most recent outing.
