The 19-year-old’s contract at the Britannia Stadium was due to expire next month, which led to interest from Tony Mowbray’s side.
However, Tony Pulis has managed to convince the youngster to remain at the Potters, extending his deal until 2014.
The Belgium Under-21 international joined Stoke from Portsmouth in 2010, after turning down offers from Manchester City and Fulham.
Cuvelier spent time last season on loan at Walsall, where he scored four goals in 18 games for the League One outfit.
And the youngster could be set for another temporary move, with Middlesbrough leading the chase for his signature.
His agent, Alex Levack of Sidekick management, told Sky Sports: "Florent is happy to have everything completed, despite interest from elsewhere," his agent.
"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."