The 20-year-old scored 11 goals while on loan from PSG last season to help Brendan Rodgers' team secure historic back-to-back Trebles.
Rodgers told the Celtic website: "We are delighted to make such an important signing. Odsonne is one of the best young players I have worked with and one of the best in Europe.
"Our fans saw exactly what he is capable of last season and we look forward to working with him again as we look to build on the tremendous success we achieved last year.”
