Co-sporting directors Laurence Stewart and Paul Winstanley told the club's website: "Axel has showcased his quality over several seasons in France and that has deservedly led to recognition on the international stage.
"He is ready to take the next step in his career and we are delighted that will be with Chelsea.
"We welcome him to the club and look forward to him joining up with Mauricio Pochettino and his new teammates in the days ahead."