The Potters have captured the left-back on a season-long loan deal from Dynamo Kiev.
The 27-year-old first caught the eye of Tony Pulis when the two sides met in the Europa League last season.
Pulis told the club's official website: "Goran really impressed me last season. He's an experienced player for his age and he has a great left foot on him.
"Naturally gifted left-sided players are like gold dust, so he will give us strength in depth down that left hand side which can only improve us.
"It's a season-long loan, so we have got a good opportunity to see how he adjusts to English football before we make a commitment to signing him."
Popov, who has won 41 caps for Macedonia, joined Kiev in 2010 on a five-year contract.