Cleverly, who has moved back down from an unsuccessfully short spell at 200lbs, says an official announcement is close for the 28 year-old to travel to Germany in the summer to face his former mandatory challenger in his own backyard.
“Terms have been agreed,” Cleverly told BBC Radio Wales Sport.
“It’s just a matter of me getting this next fight out of the way and then we are going to make an announcement.”
On fighting away from home comforts, Cleverly added: “I think I’ll quite enjoy that, it will be good. It will probably take that edge off, that pressure off, of the home crowd behind you, so it’s just a matter of going out, being ready, being focused and ripping that title from him.
“I genuinely believe I’m going to do it.”
Braehmer, 36, famously pulled out of a WBO challenge against Cleverly, after which he was stripped of the title, although the German has since proven his class with a series of defences of the WBA championship.
Prospective opponent Cleverly is now expected to have a warm-up fight on May 30 in the UK before facing Braehmer for a potential second world title reign and says he feels better now that he is back at his old weight of 175lbs.
“It’s going good, my head’s on it,” said Cleverly. “I feel focused, fit, ready, making the weight quite comfortably to be honest, it’s coming down nice.”