The 25-year-old was reportedly a target for Real Madrid and Chelsea after his performances for last season's UEFA Champions League semi-finalists and for Brazil at the FIFA World Cup.
However, he has signed a long-term contract at Liverpool after the Reds agreed a fee which could rise to $A115 million with Roma on Friday (AEST).
The fee - an initial $A99 million with a further $A16 million in potential add-ons - eclipses the $A61.3 million that took Ederson from Benfica to Manchester City in 2017, which was the most any club had paid for a goalkeeper, in sterling, at the time.
Alisson is set to take over as number one from Loris Karius, who came under fire after his mistakes led to two goals in the 3-1 UEFA Champions League final defeat to Real Madrid in May.
The Brazilian made 37 Serie A appearances for Roma in 2017-18 and shone during the club's run to the last four of Europe's premier club competition, where they lost 7-6 on aggregate to Liverpool.