Liverpool have completed the signing of Alisson on a six-year contract after agreeing with Roma on a world-record transfer for a goalkeeper.
Roma confirmed Liverpool will pay a €62.5 million (£56m) fee, surpassing the €40m (£34.7m) Manchester City paid Benfica for Ederson in 2017.
The deal could rise to as much as €72.5m (£65m), with a further £10m in add-ons, which sources told ESPN FC are dependent on Liverpool's qualification for the Champions League and wins in various competitions in the future.
"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," Alisson said in a club statement. "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 25-year-old had been a long-term target at Liverpool, whose goalkeeping situation has remained unclear after Loris Karius' errors in the Champions League final defeat to Real Madrid in May.
Alisson, who started for Brazil at the World Cup, moved to Roma in July 2016 for €8m from Internacional, and the Brazilian side are set to receive a windfall of €2.5m (£2.2m) from this latest transfer, a source said.
Sources also said that in May, Roma put a £90m valuation on the goalkeeper -- who also drew interest from Chelsea and Real Madrid -- before lowering their asking price to £75m last month.
Alisson kept three clean sheets at the World Cup, though Brazil were eliminated in the quarterfinals with a loss to Belgium.
Liverpool boss Jurgen Klopp said he was thrilled with the opportunity to land a goalkeeper of Alisson's talents.
"At one point in the last few weeks it came up, the opportunity to sign one of the world's best goalkeepers -- then it's not a long thought, to be honest, it's only that you need to have a little talk with the owners! They were quite excited, so we did it," he said. "The full package is just good.
"How we all do, he needs to adapt to the English Premier League, that's how it is. The league is different, the refs are different, the goalkeeper life is different in the Premier League.
"Age-wise he can improve, the best years are coming in the goalkeeper life, so it's all good."
As a result of the move, Liverpool are expected to push through with a move that will send goalkeeper Danny Ward to Leicester City. A source confirmed earlier on Thursday that the clubs are in talks on a £12.5 million deal.