The 25-year-old signed a long-term contract with the Reds after undergoing a medical and completing the formalities of his switch at Melwood today.
Upon putting pen to paper, the Brazil international told Liverpoolfc.com: "I'm really happy, it's a dream come true to wear such a prestigious shirt for a club of this size that is used to always winning.
"In terms of my life and my career, it's a huge step for me being part of this club and this family.
"You can be certain that I'll give my all."
Alisson, who began his career with Internacional in his homeland, was Brazil's No.1 at the World Cup in Russia this summer.