Hazard, the 21-year-old younger brother of Blues star Eden, moved to the Bundesliga side at the start of the season and, with his Chelsea deal expiring in the summer, he will now stay until 2020.
Chelsea have retained a buy-back option on the Belgian, who also spent two seasons on loan with Zulte Waregem.
Gladbach's sporting director Max Eberl said: "Thorgan has shown what a great talent he is over the past few months
We are delighted we have managed to sign him, and that he has decided to play for Borussia over the next few years."
A Chelsea statement read: "Thorgan Hazard has today signed for Borussia Monchengladbach, with Chelsea having the right to exercise a future buy-back option
"Chelsea Football Club wishes Thorgan well for the future and will continue to monitor his progress."
Hazard will formally complete his move on July 1.
Source : PA
Source: PA