The 25-year-old Morocco international had been linked with a move to a number of clubs, with QPR understood to have expressed an interest in him.
But former R's manager Mark Hughes has won the race to sign him as he looks to bolster his Stoke squad before the close of the transfer window.
Hughes said: "Oussama had a few options and I'm delighted he has chosen to join us. He's an exciting player, who has great pace and is very direct and will certainly add another dimension to what we already have at the Club."
Assaidi added: "I spoke to the manager here, he told me his hopes for the season and how he sees me fitting into the team and he made it a very attractive move for me.
"He plays football the right way, the way that I want to play, and it was quite an easy decision for me to make in the end.
"I came to the game on Saturday and watched the match and I was impressed. I feel I can fit in here well and help the team to progress."
Chief Executive Tony Scholes said: "Mark identified the need to add more pace to the team and Oussama certainly fits the bill in that regard.
"He is an exciting talent and will certainly strengthen the resources at Mark's disposal this season."
Assaidi, who joined Liverpool from Dutch club Heerenveen last August, becomes Stoke's fourth transfer window signing following Erik Pieters, Marc Muniesa and Juan Agudelo.