The 34-year-old rapper from Gary, Indiana, was arrested on June 2 before a planned concert in the French city of Toulouse.
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-euro bail last week.
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.
- with AFP