The 23 year old had been linked with The Potters for some time and in true Stoke fashion, they made there move on deadline day.
Nzonzi joins Charlie Adam and Maurice Edu as new faces at the Britannia Stadium, the fee is believed to be an initial three and a half million, rising to five.
The French midfielder had been out of the picture at Ewood Park after he submitted a transfer request, he joined Rovers in 2009.