UFC officials confirmed the bout to ESPN.com on Saturday. The event, UFC 173, will take place at the MGM Grand Garden Arena in Las Vegas.
"I've fought Anderson Silva twice, arguably the greatest ever, but I look forward to this new challenge," Weidman told ESPN.com's Franklin McNeil. "I will approach this fight like I always do and hope for the best: that I come out victorious."
Weidman (11-0) won the 185-pound title in a stunning second-round knockout over Silva at UFC 162 last July. The loss was Silva's first in the Octagon, ending his UFC-record 16-fight win streak.
Weidman repeated the feat in December, defeating Silva via TKO in the second round of an immediate rematch for his first title defense. The finish came when Silva suffered a serious leg injury as Weidman checked one of his kicks.
A former light heavyweight champion, Belfort fought for the middleweight belt in February 2011, losing to Silva via first-round knockout. He fought for the 205-pound title against Jon Jones in September 2012, and lost via submission.
Belfort is expected to apply for a therapeutic use exemption for testosterone replacement therapy in Nevada, where he tested positive for steroids in 2006. He has been granted a TUE prior to his last three fights, all of which took place in Brazil. Several members of the Nevada State Athletic Commission have expressed doubt over whether he'll be granted the TUE in Nevada due to the positive test.