Johnson recently announced that he would not be extending his contract with Hoffenheim at the end of the season, bringing an end to his three-year stint at the club.
The 26-year-old USA international has now agreed a four-year deal to join Gladbach, and director of sport Max Eberl is "delighted" to have secured his signature.
"Fabian Johnson is a very interesting player and he's available on a free transfer. He can play down both sides, both defensively and offensively, and we're delighted he has chosen to join us," Eberl is quoted as saying by PA.
Hoffenheim and Monchengladbach played out a 2-2 draw when they met each other on Saturday.