Off contract from Fulham, the goalkeeper signed yesterday in a Bosman deal.
He told chelseafc.com: "It's always been a special club. I know the area very well so it's been a dream of mine to come over to this side and it's finally happened. There were some talks a few years ago when I was a bit younger and for whatever reason that didn't come about but I'm here now.
"I'm really excited to be involved and looking forward to trying to impress and help the team as much as I can.
"Coming off the back of last season and playing a lot of games at on loan at Middlesbrough, I wanted a new challenge. I'm excited to be back in London and to be part of a massive side after the success the guys had last year.
"It's something that I want to be a part of as well so I'm really happy to be here and hopefully we're going to have another great season."
Bettinelli spent last season on-loan with Middlesbrough.
He continued: "I played a lot of games last season and now I'm sure there will be a different role for me but I'm excited for it. I'm going to try to learn as much as I can, help the team as much as I can and do everything in my power to benefit everyone else.
"It was important that I played a lot of games last season. It kept me sharp and if I'm ever needed this season then I'll be ready."
On working alongside Edouard Mendy and Kepa Arrizabalaga, Bettinelli stated: "I'm excited to work with those two top-class goalkeepers and I'm sure I'll learn a lot from them both. One of the biggest reasons for joining Chelsea is I've still got a lot to give. I'm only young in terms of a goalkeeper's point of view so the fact I can learn from two keepers that have done so much in the game already even though they're still quite young, really excites me.
"I know the coaching staff and the club has a pedigree of top goalkeepers so I can't wait to be a part of that."
The goalkeeper concluded: "It's unbelievable the fact I'm signing for the European champions! I've experienced a little bit of the step up before with Fulham when we got promoted but being involved in the Champions League and playing for a massive side like Chelsea is something that I've dreamed.
"This is one of the biggest clubs in the world so I'm really thankful to be here now. I have this amazing opportunity so it's down to me to impress and do what I can."
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