At one point the highly-rated midfielder had been linked with Arsenal, and was on loan with Palermo’s fellow Serie A side Parma in the first half of the current campaign.
But the 21-year-old has now signed a four-and-a-half-year deal with the Bundesliga strugglers.
General manager Andreas Muller told Deutsche Pressagentur: "He is a quality player and has the ambition to become even better.
"In addition, he plays in a position we have been looking to reinforce due to a list of injured players."
Acquah has made two appearances for Ghana since making his senior bow last year, scoring in the second game against Malawi.
He was not, however, included in the final squad for this month's African Cup of Nations.