The 34-year-old rapper from Gary, Indiana, was arrested on June 2nd shortly before a planned concert in the south-western 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.
He was released on €50,000 bail last week.
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.
Gibbs "has no intention of escaping justice, whether French or Austrian," he said.
Malka said the rapper, who categorically denies the rape allegations, 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.
The alleged incident took place after Gibbs who is signed with ESGN Records, had been performing last June in Vienna's Grelle Forelle club.
He reportedly invited two female fans backstage after the show, where they took liquid drugs provided by the rapper and became dazed and drowsy, according to APA.
The two women then went back to the hotel where Gibbs and his crew were staying, which is when the rapper and one of his security staff allegedly took advantage of their impaired state and carried out the attack.
After one of the women remembered the incident she went to the police who began investigating Gibbs and his employee.