The 23-year-old Switzerland international told the club's official website, www.stokecityfc.com: "It is very important for me to have the coach behind me showing great belief in me, and Mark Hughes has done that.
"He's a great guy, a great coach and somebody that I'm excited to work for.
"We have had many conversations, spoke about lots of different things and in the end, this was the move that I really wanted to make.
"It is the perfect move for me. Everything about it fits and for me, it is the perfect decision.
"I really want to show him and the rest of staff, players and supporters great football on the pitch and hopefully help move the club forward."
Shaqiri also revealed the quality of the players already in Hughes' squad helped to influence his decision.
He said: "It wanted to sign for a club with a progressive attitude and with quality already inside the building, and Stoke City has that right here.
"Stoke have some very good players at the club they are growing stronger and stronger, which is hugely important.
"I am sure that we will make a very good season together, play good football and show the supporters some really exciting times."