Macedonian international Popov ends Baggies boss Steve Clarke's search for a new left-back to provide competition for current first choice Liam Ridgewell.
The 27-year-old has become Albion's sixth signing of the campaign after being granted a work permit and passing a medical.
Clarke has moved for Popov after losing out to Everton in the battle to sign Bryan Oviedo from FC Copenhagen.
He said: "I've said many times over the past few weeks that we've been looking to bring in one more defender and I'm delighted we've managed to sign Goran.
"We allowed two left-backs (Nick Shorey and Joe Mattock) to leave at the end of last season so it's very pleasing we've got another naturally left-sided player within the group to give us more balance. We've now got good competition for places in all areas of the squad."