Jurgen Klopp believes Liverpool have signed "one of the world's best goalkeepers" after securing the services of Alisson in a world-record deal.
It is understood the Reds have agreed to pay £56million up front, with £53.8m going to Roma and £2.2m to the Brazil international's former club Internacional.
They will pay a further £9m in add-ons, dependant on Champions League qualification and also wins in that competition, Europa League or Premier League.
Although they have smashed the existing fee for a goalkeeper, which was the £35million Manchester City paid for Ederson, the fee is well below the £90million Liverpool were quoted by the Serie A club in May.
It is understood Roma dropped the price to £75million last month but a deal was able to be struck for a total of £65million, including bonuses.
A swift conclusion to the transfer was necessary as Chelsea were interested, but the Blues had to finalise the future of Real Madrid target Thibaut Courtois before they could act and that allowed Liverpool to steal a march on their Premier League rivals.
Reds boss Klopp believes he has secured the services of one of the game's top keepers.
The German said: "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. 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."
The man himself says it's a dream come true to join the Anfield club.
"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," he added. "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."
Alisson started all five of Brazil's matches and kept three clean sheets at the recently-completed World Cup, where the South American superpowers were knocked out by Belgium in the quarter-finals.
He was also a virtual ever-present for Roma last season as they finished third in Serie A and reached the Champions League semi-finals - knocked out 7-6 on aggregate by Liverpool.
It is the second major transfer between Liverpool and Roma in 12 months, the Reds having bought Mohamed Salah for what turned out to be a cut-price £38million after the Egypt international scored 44 goals last season.
Alisson's arrival, following on from that of midfielders Naby Keita and Fabinho, and winger Xherdan Shaqiri, is understood to have completed Klopp's business for the summer.
They have no intention of going back in for Lyon's France playmaker Nabil Fekir after a move fell through just before the World Cup despite a fee initially being agreed.
