The Congolese frontman had signed a contract to remain at Eintracht Stadion until 2016, but it was dependent on the club staying in the German top flight.
And, despite talks to hang on to Kumbela, Braunschweig confirmed on Thursday that the player had left the club.
"Despite good conversations, we could not agree on further cooperation with Domi," said sporting director Marc Arnold. "We were interested to extend with him, but our ideas were economically too far apart.
"For his sporting and personal future, we wish all the best to Kumba and thank him for his services shown."
Kumbela expressed his gratitude for his time at the club: "I want to thank those responsible for the harmony, the entire club and the fans for the unconditional support in recent years.
"It was a great and successful time that I like to look back on.
"But towards the end of my career, I would like once again to look for a new challenge."
Kumbela scored 64 goals in 164 games for Braunschweig.
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