The Reds said he had signed "a long-term contract", with British media reports saying Shaqiri had arrived at Anfield in a five-year deal for ?13 million ($17 million, 15 million euros).
The 26-year-old winger's move follows Stoke's relegation from the Premier League.
"I'm very happy to be here. It's a huge club with big history, big players and a fantastic coach (Jurgen Klopp)," Shaqiri told liverpoolfc.com.
"I want to improve myself too, I want to be with the best and I want to win titles. That's what I'm here for."
Shaqiri, who was born in Kosovo but moved to Switzerland as a child, has just returned from the World Cup in Russia where his country were eliminated in the last 16 by Sweden.
He sparked controversy by celebrating his goal in the 2-1 win over Serbia in the group stage by making a gesture with his hands to represent the two-headed eagle of the Albanian flag with which many Kosovars identify.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)