The 60-year-old Swiss tactician told a post-match news conference he had just overseen his last game at the helm, while a statement from the club said they had accepted an approach for Favre.
"It is the end of an irregular season, where fortunately we took our hopes of European qualification to the end," the former Borussia Monchengladbach coach said.
"It was my last game in charge of Nice tonight. These were two fantastic years at Nice, at the human and sporting level."
Favre refused to confirm whether he was going to Dortmund to replace the outgoing Peter Stoger , despite Kicker reporting he has agreed a two-year contract.
"I am leaving Nice, but I cannot say more. Quite simply, I cannot say more," he added.
Nice president Jean-Pierre Rivere wished Favre luck in the "new challenge that awaits him".
"During his two seasons with us, Lucien has helped to keep Nice growing, with an exceptional track record last year," he said.
"We thank him for the quality of the work he has done at the helm of the team and for his constant investment.
"He is a professional and a man of great quality. We wish him the success he deserves in the new challenge that awaits him."
Favre's successor at Nice is likely to inherit a squad in transition, with forwards Mario Balotelli and Alassane Plea both expected to leave the club and further bids anticipated for midfielder Jean Michael Seri.