Liverpool have made Roma's Alisson the world's most expensive goalkeeper by signing him on a six-year deal.
The Reds have not revealed how much they have paid for the Brazil number one but Roma said the deal is worth up to £66.8m (72.5m euros).
"In terms of my life and my career, it's a huge step for me being part of this club and this family," said the 25-year-old.
He has been at Roma for two years, playing 37 Serie A games in 2017-18.
'One of the world's best goalkeepers'
Liverpool manager Jurgen Klopp said he has signed "a real personality".
"At one point in the last few weeks it came up, the opportunity to sign one of the world's best goalkeepers," he added. "The owners were quite excited, so we did it.
"He has nothing to do with the price, we have nothing to do with the price. It's the market, that's how it is and we will not think a lot about it.
"He needs to adapt to the English Premier League. The league is different, the refs are different, the goalkeeper's life is different in the Premier League.
"We got him here because of his existing strengths, which is in all goalkeeper departments the highest level."
Alisson said the move was a "dream come true" and revealed Liverpool forward Mohamed Salah, who he used to play with at Roma, had sent him a message before he completed the move to Anfield.
"Yesterday, he sent me a message saying: 'Hey, what are you waiting for?' As the negotiations were at an advanced stage, I replied to him straight away saying: 'Calm down, I'm on my way!'
"I'm really happy to have the opportunity to play alongside him again. As well as being a great player, he is a huge character and a great person - which is the most important thing."
Alisson is Liverpool's fourth major signing since they finished the 2017-18 season fourth in the Premier League and were beaten by Real Madrid in the Champions League final.
Brazil midfielder Fabinho, 24, has joined from Monaco in a deal which could be worth more than £40m, while Guinea midfielder Naby Keita, 23, has moved to the Merseyside club from German side RB Leipzig in a £48m deal.
Liverpool have also signed Switzerland forward Xherdan Shaqiri, 26, from Stoke City after triggering his £13m release clause.
In addition, 26-year-old forward Salah - who has scored 44 goals in 52 appearances for the club - signed a new five-year contract this summer.
World's most expensive goalkeepers
The previous record fee for a keeper was the 53m euros paid by Juventus to Parma for Gianluigi Buffon in 2001.
The Premier League record for a keeper is the 40m euros Manchester City paid Benfica for Ederson in June 2017.
Buffon's deal was worth £32.6m at the time, while Ederson's was worth £35m because of changing exchange rates, but as most deals between clubs in Europe, including the Premier League, are completed in euros Buffon's deal is recognised as the record.
Find all the latest football transfers on our dedicated page.