The former Birmingham keeper made 45 appearances for City last season but was ready to play understdudy to Adrian when the Irons moved in.
Speaking to the official West Ham website he said: ‘My initial reaction to joining West Ham is excitement.
‘It was a tough decision turning down Birmingham’s offer of a new contract because of the second part of the season we had and the team we had built.
‘I started at Charlton when I was 16 and left when I was 23,’ he explained.
‘It has been a long journey to try get back to the Premier League and a great achievement to be able to do so. It is where players all around the world would like to be.
‘I’ve played for the last five seasons so I would like to think I can come in and challenge for a place in the team. Adrian’s had a fantastic season so it is going be tough, but it is a challenge I look forward to.’