And the left-back admits that the Everton manager was a driving factor in his decision to pen a five-year deal on Merseyside.
The 25-year-old told Evertontv: "I want to show my best football here and discover the best league in the world". I progressed a lot as a player and as a person by playing with the best players in the world.
Stoke are hoping to win promotion back to the Premier League this summer and see Williams as the ideal option to strengthen their backline on the cheap.
And he sald: "It's a little bit daunting, this being my first loan move, but I'm excited and looking forward to seeing what it brings". Immediately I said, 'I want to come to Everton'.
"Thanks to all the physios, the staff with whom I have worked, the physical trainers, the security people, all that make the club a family".
It simply says "I never walk alone", bearing a remarkable resemblance to Liverpool's club anthem, You'll Never Walk Alone.
He wrote on Instagram: "I want to say thank you very much to all. That is what is important and I could not be more excited about this challenge".
Signing Digne gives them great depth at left back with Leighton Baines expected to be his cover, but the other areas of the team still need work.
The 25-year-old France global joins Everton after two seasons in Barcelona, where he made 46 appearances across all competitions.
Digne will be seen as the long-term replacement for Leighton Baines, who turns 34 in December and only managed to feature 22 times in the Premier League last term. "This is his mentality having captured titles in his career and having these on his resume".