The 29-year-old, who has played 50 times for his country, left Barcelona at the end of last season after four years.
"It's no secret that Ibrahim was wanted by a number of clubs and we are understandably delighted that he has chosen to join us," Stoke chief executive Tony Scholes told the club's website.
"He's clearly excited about the prospect of playing in the Premier League and the fact that he knows so many players who are already at the club will no doubt help him settle into his new surroundings."
Afellay started his career with PSV Eindhoven and helped the Netherlands reach the 2010 World Cup final before joining Barca.
The Spanish giants won the Champions League in 2011 but Afellay's career in Spain was stalled by injuries and he was sent out on loan to Schalke 04 from 2012-13 and Olympiakos last season.
Afellay was Stoke's eighth signing of the close season after Philipp Wollscheid, Jakob Haugaard, Joselu, Marco van Ginkel, Glen Johnson, Shay Given and Moha.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
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