The 20-year-old, who has put pen to paper on a three-year contract, could go straight into David Weir's squad for Tuesday night's Johnstone's Paint Trophy tie at Scunthorpe.
Cuvelier, who played alongside Febian Brandy while on loan at Walsall last season, joined Stoke from Portsmouth in July 2010 but failed to make the first-team breakthrough at the Britannia Stadium.
The attacking midfielder, born in Anderlecht,
first arrived in England in 2008 when he joined Portsmouth's Academy and moved on to Stoke in the summer of 2010.
The former Belgium Under-19s captain made a total of 40 appearances in two separate loan spells for Walsall and made one appearance for Peterborough while on loan at London Road for a month late last season.