Assaidi completed a season-long loan switch to the Potters from Liverpool, whom he joined a year ago from Dutch side Heerenveen.
The 25-year-old Morocco international made only four appearances in the Premier League - all as a substitute - for the Reds last term, as well as featuring eight times in cup competitions.
Assaidi could make his Stoke debut in Wednesday night's Capital One Cup second-round home clash with Sky Bet League One outfit Walsall.
He told his new club's official website: "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.
"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."
He added: "I spoke to the manager here (Mark Hughes) and he told me his hopes for the season and how he sees me fitting into the team.
"He made it a very attractive move for me to be honest.
"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 (Stoke's 2-1 Premier League home win against Crystal Palace) and watched the match and I was impressed. I feel I can fit in here well and help the team to progress."
Hughes has stressed his intention to field a "strong" team for the Walsall match.
The Potters - then managed by Tony Pulis - were beaten by a visiting third-tier side in the second round of the competition last year as Swindon emerged after extra-time with a 4-3 victory at the Britannia Stadium.
Pulis had made six changes to his first XI on that occasion and his successor Hughes, wary of not giving the opposition enough respect in terms of selection, says he is only looking to make "one or two" adjustments from the Palace victory.
"I don't give up competitions lightly," Hughes said.
"We want to do well in it and we want to progress in it, so I'll be putting out a strong team. There will be one or two changes but nothing wholesale."
Fit-again Stoke pair Wilson Palacios and Brek Shea are poised for a return to first-team involvement, but fellow midfielder Jamie Ness (thigh) is not yet ready to feature.