The 19-year-old has signed a contract with the Foals until June 2017 and will arrive at the club when the transfer window opens on 1 January 2014.
"We're happy that Kwame has decided to join us," commented Borussia's sporting director Max Eberl. "He has great potential and is exactly the type of player we're looking for in terms of scouting for talent."
Yeboah, who will be based at the club's academy at the Borussia Park, has signed a professional contract but will initially be part of the reserve squad. "He'll receive all the time he needs from us to get used to his new surroundings," said Eberl.
The player himself was delighted to have rubber-stamped a move to one of the world's top leagues. "It's a big step for me in my still young career," he said. "The Bundesliga is shown on TV here in Australia, so Mönchengladbach are certainly a team I'm familiar with."
Before he makes the journey to Europe, Yeboah - no relation to the legendary Anthony Yeboah, who played for Eintracht Frankfurt in the 1990s - will make his final appearance for Brisbane Roar away at Sydney FC.
Born in Australia, but with Ghanaian descent, he is eligible to represent both nations at international level, but has yet to appear in international competition.