The deal has now been confirmed, with the Belgian left-back having signed a three-year contract at The Hawthorns.
Speaking about his latest recruit, head coach Alan Irvine told the club's official website: "Sebastien is an experienced left-back who has played at a high level for many years. After being named in Belgium's provisional World Cup squad, he just missed out on Brazil, mainly because he hadn't played enough games towards the end of the season.
"He's joined us with a real hunger to prove himself at Albion and get back into the international setup. We've done our due diligence on Sebastien in terms of people who have worked with him, including Romelu Lukaku and Kevin Mirallas.
"You make your own mind up about a player's ability from watching him play but you put these calls in to find out about their personality. The feedback on Sebastien was very positive."
Pocognoli will report to pre-season training with his new teammates on Monday.