The professional football club terminated their contract with Gary Rowett on Tuesday.
Now, Jones has signed a three-and-a-half-year contract at Stoke.
The former Luton boss promoted his club from League Two last season, having been appointed in January 2016. He had previously worked as coach and then assistant manager at Brighton.
“We’ll try to play in a certain way which I will work religiously on,” said Jones after his appointment. “This is not just a job for me, this is a lifestyle.
“Once we get our philosophy implemented, and we get working with the players, we aim to get the best out of them.”
Jones has earned a reputation for his brand of expansive football, with Luton scoring 301 times while conceding just 174 in his 170 matches in charge.
“Nathan is an incredibly driven and passionate individual and we are delighted to have secured his services for Stoke City,” Stoke owners John Coates and Peter Coates said in a statement.
“We have been following Nathan’s career for some time and when we met him were hugely impressed with his clear vision as to how he will achieve success at Stoke.”