The 26-year-old heads to the Bundesliga just over a year after Celtic banked around £17million from his move to the Serie A side.
Kuhn enjoyed a successful spell at Parkhead following his arrival from Rapid Vienna, with his performances for the Hoops earning him a lucrative switch to ambitious Como.
However, the German struggled to establish himself under Cesc Fabregas in Italy , making just six league starts and registering one goal and one assist.
Kuhn was then left out of Como's squads at the beginning of this season, paving the way for his return to his homeland with Borussia Monchengladbach.
"It has always been my goal to play in the Bundesliga and I am very happy that it is now going to become a reality," Kuhn said.
Gladbach sporting director Rouven Schroder believes the former Celtic attacker will add several qualities to their forward line.
"Nicolas is left-footed, versatile in attack, fast, can solve one-on-one situations, and is also dangerous in front of goal.
"He has proven all of this in his career, not least on the European football stage."
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