The deal, which has the option of an extra 12 months, potentially takes Cuvelier through to the end of the 2014-15 season at the Britannia Stadium.
He told his club's official website: "I am absolutely delighted to have agreed a new contract here and I am already looking forward to the new season. This is another big step in my career, and my next aim is to work as hard as I can to impress the management and then hopefully get a chance in the first team."
The 19-year-old Belgian - having attracted interest from the likes of Manchester City, Tottenham and Fulham - opted to join the Potters from the youth ranks at Portsmouth in 2010 and he is yet to make his first-team debut for the Staffordshire club.
Cuvelier spent the second half of the 2011-12 campaign on loan at npower League One outfit Walsall, for whom he scored four goals in 18 appearances.
He said: "The loan spell I had with Walsall has really benefited me, and I do feel a better player because of that.
"Playing in front of 20,000 supporters at the likes of Hillsborough and Valley Parade has whetted my appetite to succeed more than ever, and I will be working as hard as ever to impress (Stoke manager) Tony Pulis and the rest of the backroom staff."
He added: "There were offers from other football clubs so this was a big decision for me, but I am certain that I have made the right choice."
