The Belgium Under-21 international has yet to make a first team appearance for the Potters.
Posh boss Darren Ferguson said: "He is a very good technical player who can play anywhere in midfield."
Ferguson told the club website: "He has been with Walsall this season and did very well. We thought we could perhaps do something for next season, but obviously it has been accelerated because I have injuries to Davide Petrucci and Alex Pritchard, so that has made my mind up.
"He wanted to come here, he plays football the right way and I believe we will suit each other. He will go straight into the squad on Saturday for the game with Cardiff City at London Road."
Cuvelier said: "It happened very quickly, but I am really pleased to be at a big club like Peterborough. I felt the time was right to play in the Championship."