The 25-year-old has signed a four-year contract with the Barclays Premier League club and will begin life at Anfield as understudy to Jose Reina.
Cavalieri, who also holds an Italian passport told www.liverpoolfc.tv: "I know it won't be easy to get into the team. I watched some Liverpool games in both the Premier League and Champions League last year and I know Pepe (Reina) is a very good goalkeeper, but everyone has to fight for their place and I'm sure we will have a healthy rivalry."
He added: "I know I will have to be patient and work very hard to achieve my aims - but it is always like that when you come from another country.
"You have to adapt inside and outside of the pitch and get used to the way things work. But with hard work you get there.
"My confidence has got me where I am today and maybe people are aware of what I did at Palmeiras in Brazil.
"I am sure that one day I can get the number one position but that will only come with hard work."
Meanwhile Liverpool have agreed a fee with Newcastle United for the transfer of Danny Guthrie to the north east.
The former Academy player, who spent last season on loan at Bolton, will now discuss personal terms with Newcastle boss Kevin Keegan before finalising the deal.
A Liverpool spokesman said: "We have agreed a transfer fee with Newcastle United for the transfer of Danny Guthrie. We have now given Newcastle permission to speak directly with the player."