They were due to meet in 2011 before an eye injury forced Braehmer to withdraw.
The German will be aiming for a seventh successful defence of his title.
"This fight has been destined to happen and I can't wait now," said Cleverly, a former WBO title holder who has won 29 of his 32 professional bouts.
"Juergen is a great champion and an underrated one.
"He's a puncher that has pedigree in the pros and all the way back to the amateurs, he's a proper professional and a credit to the game.
"I am going into the champion's backyard and I need to rip the title off him, and that's what I intend to do."
Breahmer, who has lost only twice in a 50 fight career, said he is looking forward to the fight.
"In boxing you can never say never," he said.
"This is a fight the fans have wanted to see for a long time and I'm happy it's finally happening.
"I look forward to meeting Nathan Cleverly in the ring at the Jahnsportforum and proving once and for all who is the better boxer."
Cleverly's last fight was a points defeat by Andrej Fonfara in Chicago in October 2015.
The WBA super world light heavyweight title - the body's top honour in this weight division - is held by Sergey Kovalev, who stopped Cleverly to win the WBO crown in 2013.
Welsh former World champion Nathan Cleverly will challenge Juergen Braehmer for the WBA regular light-heavyweight title in Germany on 1 October.