The 25-year-old Moroccan winger joined the Merseysiders from Heerenveen in summer 2012 but failed to make an impact at Anfield.
Assaidi has now signed a season-long deal with Stoke.
"It was frustrating last season, especially having not been given too many opportunities on the pitch, but I am here now and I am looking forward to playing in the Premier League," he told the club's official website.
"When I did play last season I thought I did well, and the experiences I did have on the field has given me an understanding of what to expect in the Premier League."
Stoke are in Capital One Cup action on Wednesday when they entertain Walsall in the second round of the competition.