Clarke, a versatile left-sided defender, has signed a four-year deal after a fee of £275,000 was agreed between the two clubs.
He told the official West Ham site “When I knew that West Ham United were interested I was really keen to come.
“I had some great times at Stoke, but it’s been a dream of mine for some time now to play in the Premier League and I’m delighted that West Ham have given me that chance.
“I first heard about the Club’s interest about two or three weeks ago, and I’m just pleased that everything’s been sorted out now and I’m a West Ham United player.
“Now I just want to get stuck into training and try and impress the manager enough to get a place in the team.”