The German international will move to Stamford Bridge when the transfer window opens again in June and has penned a five-year deal.
He told Bild: "There is nothing greater than Chelsea. I'm very happy the transfer worked."
Meanwhile, Bremen sporting director Klaus Allofs stated that Marin had not developed into the player they had expected him to after joining from Borussia Monchengladbach.
He also expressed his belief that the attacker's style did not suit the German outfit and indicated that he had rejected a new contract at the Weserstadion.
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Allofs said: "Marko's development was not what we had imagined. He has his strengths, but they are not the ones we need at the moment. An extension was not an issue as he indicated to us."
The sporting director went on to rule out Chelsea striker Romelu Lukaku coming in the other direction, but suggested another Blues player could be on the move
He added: "Chelsea have other plans, but I will not rule out another player coming to us."
Marin’s team-mates at Bremen also had their say on the move, claiming the 23-year-old will have no problem adjusting from the Bundesliga to the Premier League next season.
Brazilian centre-back Naldo said: "Marko is always dangerous with his dribbling. This may work well for him in England."
Whilst Sebastian Prodl added: "Chelsea will have something to think about, he won't grow any more. And he cost €10 million. He lacks strength, but he is nimble enough to compete against physically strong defences."