Mancienne and fellow centre-half Slobodan Rajkovic were recruited on four-year deals, midfielder Jacopo Sala signed a three-year contract and another defender, Jeffrey Bruma, agreed a year-long loan.
Mancienne, 23, told the People: "It was a pleasure to be at Chelsea because I was there from being a little boy and there are great people at the club. But obviously it's disappointing at the same time because, growing up there, that's where I wanted to play. It was a little frustrating that I wasn't given the opportunity to do so but there came a time when I had to make a decision because I wanted to play regular first-team football and make a name for myself, not just be in the squad or on the bench.
"I figured coming abroad was a new challenge, a new kind of experience and something not many players have done. I saw it as something I really wanted to do anyway and then the opportunity came and I couldn't turn it down.
"Frank (Arnesen) told me everything about Hamburg but I knew before he mentioned it that they were a big club. Once the offer was on the table I knew I wanted to come here.
"It's a big opportunity - and having a few friendly faces around has made it easier.
"Where I live is really nice, everything has been built up brand new. It has loads of little restaurants, and if I want to go into town it's a 10-minute walk as well.
"The boys who have come in from Chelsea are literally round the corner. Sala, Jeffrey and Bodan live two minutes from each other and I'm only five minutes from them - just far enough.
"Three of us are having two German lessons a week. It's a difficult language to learn but I've picked up quite a lot already because I'm hearing it every day.
"I recognise words - obviously some of the swear words - and I'm starting to put sentences together. I'm OK as long as people don't talk too fast."