The defender, who joined the Baggies on loan last summer, earned over 50 per cent of the vote.
The Baggies, who were relegated back to the Championship in 2020-21 after just one season in the Premier League, sit tenth in the table.
Speaking to the West Brom's official website, Clarke said: "I’m absolutely delighted to pick up this award.
"I felt I’d come into the team and done well at the start of the campaign, but to get the injury was a setback and you obviously never know if you’re going to properly get back up to speed. I worked really hard and thankfully I wasn't out for too long.
"There's an underlying frustration from this season because as a team, and as a club, we’ve underachieved. I take all the criticism onboard which is what we have to do because that’s part of being a footballer.
"Some of the supporters have gone out of their way to vote for me and I take great pride in that. I'd like to thank them for doing so."