The 25-year-old joined the Anfield side in August 2012, but has failed to nail down a regular spot in Brendan Rodgers' starting XI and made just four Premier League appearances last season.
He joins Erik Pieters and Marc Muniesa in making the switch to the Britannia Stadium during the transfer window, while American striker Juan Agudelo has agreed a January switch.
And manager Mark Hughes believes the Morocco international can offer Stoke a different option to what they currently have at their disposal.
"Oussama had a few options and I'm delighted he has chosen to join us," Hughes told Stoke's official website.
"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 joined Eredivisie side Heerenveen in 2009 after successful stints at Almere City and De Graafschap before moving to the Premier League a year ago.
He will hope to feature in Stoke's visit to Upton Park to face West Ham on Saturday.
Alexia Putellas: "We’re already the only club to have won the men’s and women’s Champions League, so the only thing even more historic to do than that would be to win it in the same season"
‘Trent has won everything he can for Liverpool, but of those who’ve left that we wanted to stay, who’s actually done better? I can only come up with one’: Reds legend highlights potential danger of Alexander-Arnold moving to Real Madrid
