The 26-year-old has signed a four-year deal with the Spanish side, who have inserted a 30million euro (??21.5million) buy-out clause in his contract, after undergoing a medical on Thursday morning.
“Sevilla FC and Stoke City have reached an agreement for the transfer of midfielder Steven Nzonzi, who arrived in Seville on Wednesday night,” said a statement on sevillafc.net.
“The player has signed for four seasons and will have a buyout clause of 30 million euros.”
It was reported earlier on Thursday that the Potters had accepted the bid from the Europa League winners after an initial offer of ??3million was rejected last month.
N’Zonzi, 26, had a year left on his Stoke contract and chief executive Tony Scholes previously stated he and the club had hoped the former Blackburn would sign a new deal.
But manager Mark Hughes confirmed N’Zonzi was discussing his personal terms with the Spanish side and the deal has now been finalised.
A statement on Stoke’s website said: “The club would like to place on record it???s thanks to Steven and offer him our best wishes for the future.”
Hughes said on Wednesday: “It’s been well documented there’s been interest from Sevilla.
“We’ve got to a point where the club is comfortable with the deal Sevilla have come up with, so we’ve given Steven permission to speak with them.
“We worked really hard to convince Steven his future lay here but it didn’t seem to be enough.”