Ashworth revealed Albion attempted to sign Popov two years ago from Heerenveen but he opted to move to Ukraine.
He was spotted by Hawthorns scouts while playing in Holland.
Ashworth said: "Goran first came to our attentions during our promotion season of 2009/10 but we missed out on him that summer when he joined Kiev.
"We've continued to monitor him and have seen him acquit himself well for Kiev in the Champions League and against Manchester City and Stoke in the Europa League.
"Goran is an established, experienced left-back who is tall, powerful, good on the ball and likes to get forward. I'm sure he will settle in really well with us in the Premier League."