Favre's previous deal was set to expire next year, but the club has moved to keep him at Borussia Park for a further two seasons.
After arriving at Monchengladbach in February 2011, Favre helped the club reach the qualifying stages of the Champions League in his first full campaign.
"Lucien has done outstanding work with us in the past three years," said sporting director Max Eberl. "Our (successful) relegation fight in 2011 and the return to the European Cup in 2012 are most directly associated with his name.
"Our journey together is not over yet, and we are looking forward to further cooperation."
Monchengladbach is currently eighth in the Bundesliga, eight points out of a Champions League place.