The Blues announced on their official website that they have had an undisclosed offer accepted and the Germany international has agreed personal terms to move in the summer.
The 23-year-old, who joined Bremen from Borussia Monchengladbach in 2009 and was contracted to the club until June 2013, has already passed a medical in London and will sign a contract with the Blues in the next few weeks, according to his current club.
"I had a really good time with Werder together with many great guys here, and I have lots of nice memories, but of course I am looking forward to the challenge of playing in the Premier League with such an established club," he said.
Bremen's director of sport Klaus Allofs said in a statement: "We have always said that we would be open to talk if any of our players receives a good offer which was also interesting for Werder and we had good talks with the management at Chelsea, so that we were able to reach an agreement quickly.
"In the coming weeks, we will then deal with the last formalities.
"We wish Marko all the best for this new challenge."