The 40-year-old goalkeeper made the short trip across west London after turning down a new contract at Fulham and will provide competition for Petr Cech.
|9/4||Chelsea are 9/4 with Coral to win the Premier League
"It's a phenomenal club. It's one of the biggest and best clubs in the world, and it's an honour to sign for Chelsea. I didn't take much convincing to come here," he told the official club website.
"There were other interests but once I knew Chelsea was interested it was very much the case that I wanted to try and make it happen. I'm very fortunate and delighted to be sitting here today.
"I live closer to here than my previous club. There were a lot of things that ticked all the boxes, but most of all Chelsea Football Club is an enormous club and I think a club that can re-establish itself as the best club in the country.
"It has an unbelievable manager and an unbelievable squad of players and it's very exciting."