Yeboah, 19, passed his medical and will arrive in Germany when the January transfer window opens.
He has signed a deal until June 2017 but will initially be part of the club's reserve squad and based at the academy at Borussia Park.
Borussia sporting director Max Eberl said Yeboah had the kind of talent his club looked for.
"We're happy that Kwame has decided to join us," Eberl said.
"He has great potential and is exactly the type of player we're looking for in terms of scouting for talent.
"He'll receive all the time he needs from us to get used to his new surroundings."
Yeboah caught the eye in the A-League with spectacular, powerful strikes against Central Coast and Western Sydney.
Eligible to represent both his place of birth Australia and Ghana, Yeboah's last game for Brisbane will be the Boxing Day clash at Sydney FC.
Yeboah said he was delighted to make the huge move after just 11 A-League appearances.
"It's a big step for me in my still young career," he said.
"The Bundesliga is shown on TV here in Australia, so Monchengladbach are certainly a team I'm familiar with."
Lucien Favre's Monchengladbach side sit fourth – the UEFA Champions League qualifying place – in the Bundesliga.
