The 25-year-old has been on the Premier League club's radar for a number of weeks and, on Wednesday, multiple reports claimed that a move to Anfield had been agreed.
Roma confirmed Alisson's departure at 9.30pm BST on Thursday night and, half an hour later, Liverpool followed suit in announcing the Brazil international's move to Merseyside.
The Reds did not disclose the fee involved in signing Alisson, but the Giallorossi revealed that the Selecao star moved clubs for €72.5m (£65m), a world-record fee for a goalkeeper.
"Alisson, 25, will join the Premier League side for an initial fee of €62.5m (£56m), the most expensive transfer fee ever paid for a goalkeeper," read a statement on the Roma website.
"The agreement also includes a number of performance-related clauses, on the part of both the player and the English club, that add up to an additional €10m (£9m)."
Upon putting pen to paper at Liverpool, Alisson told the official club website: "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."
Across his two seasons in the Italian capital, Alisson made 64 appearances in all competitions.