"It wasn't a hard decision for me to join Stoke, what with the squad that's already in place here, the quality of the manager and the ambition of the club. It was easy for me," Williams told Stoke website.
Stoke manager Gary Rowett was pleased with Williams' arrival as the West Midlands outfit seek an immediate return to the top tier after being relegated last season.
"Having spoken to Ashley he feels like he has a point to prove and has a real hunger," Rowett said.
The 33-year-old former Swansea City player is Stoke's sixth signing in the current transfer window following the arrivals of Benik Afobe, Peter Etebo, James McClean, Tom Ince and Adam Federici.
Stoke open their Championship campaign against Leeds United on Sunday.
(Reporting by Aditi Prakash in Bengaluru; Editing by Amlan Chakraborty)
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