The 20-year-old scored 11 goals in 29 appearances on loan at Celtic Park last season as the Hoops secured back-to-back domestic trebles.
Speaking to his new side's official website, the ex-France Under-19s international said: "From the moment I walked into Celtic, the club has felt like home to me. I have been made to feel so welcome by everyone at the club and our fans have given me such brilliant support.
"Celtic is one of the world's great football clubs and I was desperate to make my move permanent. The scenes from May when we achieved such a historic double treble and made the city come alive are still very fresh in our memories.
"To see our fans so happy is the reason you play football and now we want to do everything we can to bring our great supporters even more success."
Celtic Manager Brendan Rodgers added: "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. I am sure he will be a big player again for us this season."
Odsonne spent seven years in PSG's system without making a single senior appearance.