The trail on the long-running saga went quiet over the World Cup, with Alisson at the tournament with Brazil, but a phone call with Jurgen Klopp on Tuesday followed by a flurry of negotiations saw things move along rapidly.
Upon putting pen to paper, the Brazil international told Liverpool's official 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."
The Reds have now broken world records for the highest fees spent on a goalkeeper and a defender in the last year.
It's a startling turnaround for Jurgen Klopp, who said in the past: "Other clubs can go out and spend more money and collect top players. I want to do it differently. I would even do it differently if I could spend that money."
Chelsea were the club expected to provide the most competition for the Brazil international's services as they look to replace Thibaut Courtois, who is nearing a move to Real Madrid before next month's transfer deadline.
8 - Alisson conceded 28 league goals last season (excl. OGs), but based on Opta xG data for the shots on target he's faced, the average goalkeeper would've been expected to concede 36 goals. This was the biggest differential by a Serie A goalkeeper in 2017-18 (8). Coveted. pic.twitter.com/g8MW47pNLZ— OptaJoe (@OptaJoe) July 17, 2018
Roma only made the Brazilian a starter in their side last season, having left him to sit on the bench behind Wojciech Szczesny in his first season in Europe following a €7.5m move from Internacional.
The Italian side are expected to spend some of the profits from the move on a former Liverpool man, taking Suso from Serie A rivals AC Milan, while Paris Saint-Germain's Alphonse Areola is the most likely target to directly replace Alisson.