The 34-year-old rapper from Gary, Indiana, was arrested on June 2 shortly before a planned concert in the southwestern French city of Toulouse, one of a string of European tour dates.
Gibbs, whose real name is Frederick Tipton, was the subject of a European arrest warrant issued on May 31 for an alleged rape in Austria in 2015.
According to Austrian media, citing prosecution sources, Gibbs is accused of drugging two women who came backstage after a July 6 concert in Vienna, before taking them back to a hotel where they were allegedly raped by the rapper and one of his security agents.
Malka said his client was considering whether to appeal the extradition. He has 72 hours to do so.
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Gibbs "has no intention of escaping justice, whether French or Austrian," he said.
Malka said the rapper was opposed to the "harsh transfer procedure" and wants to freely hand himself over to Austrian authorities.
The singer was touring Europe to promote his new album "Shadow of a Doubt" and had to cancel shows in the French cities of Marseille and Strasbourg as well as in Porto, Portugal, plus the next stage of his tour in Canada.