The 33-year-old defender signed an initial one-year deal.
Ward spent five seasons with Burnley, helping the Clarets win the Championship title in 2016.
Speaking about the move, Stoke City manager Nathan Jones said:
He’s a wonderful player with great experience,
I’ve worked with Stephen in the past when he was on loan at Brighton and I know that technically he’s very, very good.
The Irish professional footballer will become Stoke City six summer addition.