The fight was confirmed today at a London press conference by promoter Frank Warren, and will go ahead on May 21st in London at the O2 Arena.
Cleverly, 23, is the current WBO interim champion after wins in his last two fights against Karo Murat and Nadjib Mohammedi.
However Braehmer represents a significant step up in class for the unbeaten mathematics graduate, who has put together a 21-fight winning streak.
Braehmer, 32, has a 36-2 (29) record and, like Cleverly, is a former European champion.
“I’m delighted that I’ve been able to secure home advantage for Nathan,” said Warren.
“It wasn’t cheap to get Braehmer over here, but it will be worth it because I really believe in Nathan and he has a big future ahead of him.
“It looked like the fight was going to go to purse bids, but we made a substantial offer the night before and it was enough to persuade Braehmer to say yes.
“Nathan has worked incredibly hard for this opportunity, and waited patiently to get his shot.
“He’s getting this fight at exactly the right time, and it could be a massive moment in his career.
“This is a huge fight. Braehmer is a proven champion and belongs at elite level, while Cleverly is young and hungry and could be the next big thing in the UK.
“Don’t forget that light-heavyweight is a very sexy division right now.
” You’ve got Chad Dawson, Bernard Hopkins, Tavoris Cloud and Jean Pascal out there, and Nathan has the chance to make a name for himself both here and in the States.
Cleverly added: “I always thought that I would get my shot at Braehmer.
“There was talk that he might be stripped or would vacate the title, but I never wanted that to happen.
“He’s the champion and the only way I would consider myself a true champion is if I took the belt from him, rather than picking up the vacant title.
“I’m going to take the fight to Braehmer, walk through him and give him some serious punishment.
“I feel that this fight has come at the perfect time for me and I want to make a big statement.
“You only have to take a look at Braehmer’s record to realise just how dangerous he will be. He’s a genuine champion and a genuine talent, but I think I have enough in my armoury to beat him.
“Before my last fight I was only sparring amateurs, but this time around I’ve got some big professional cruiserweights in and I’ve been knocking them out.
“I’m going to significantly better against Braehmer than I was against Mohammedi, and I’m predicting a spectacular performance.”