Cuvelier impressed while on loan at League One side Walsall for the latter part of the last season.
Cuvelier’s previous deal at Stoke was due to expire this summer and the youngster was strongly linked with a move to Middlesbrough.
Cuvelier could yet end up at Middlesbrough next season in a loan move.
“Florent is happy to have everything completed, despite interest from elsewhere,” his agent Alex Levack of Sidekick management told Sky Sports.
“He sees his long-term future at Stoke and is now looking to get out on loan in the Championship and work his way back into the Belgium Under-21 team.
“He has proved himself at League One level and now wants to do the same in the Championship.”
