The Belgium U21 international spent time with League One side Walsall earlier in the season and signed a new two-year deal at the Britannia Stadium in May 2012.
Cuvelier, 20, has represented his country at all youth levels and played 22 times for the Saddlers this campaign, scoring three goals and adding to the experience gained from his previous loan period at the Banks's Stadium the season before.
Anderlecht-born Cuvelier started his career as an apprentice at Mouscron in his native country, before moving to Portsmouth under Harry Redknapp in 2009.
Redknapp soon departed for Tottenham, however, and while Cuvelier was linked with a switch to White Hart Lane too, he eventually chose Stoke City in July 2010 but has yet to make his first-team debut.
Posh boss Darren Ferguson said: 'He is a very good technical player, he can play anywhere in midfield, he is two-footed and I am pleased to have him here.
"He has been with Walsall this season and did very well and he has been on the radar. 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.
"I have spoken to Tony Pulis and thank you to him for allowing us to get it done. He wanted to come here, he plays football the right way and I believe we will suit each other."
Cuvelier said: "It happened very quickly, but I am really pleased to be at a big club like Peterborough. I have been playing with Walsall and I felt the time was right to play in the Championship and I am really happy to be here."