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.
Alisson played 49 games for AS Roma last season and helped lead the Serie A club to the Champions League semi-final round, where it lost to Liverpool 7-6 on aggregate. "In terms of my life and my career, it's a huge step for me being part of this club and this family".
Alisson has been priced up at £5.5m in Fantasy Premier League, half a million more expensive than fellow Liverpool goalkeepers Loris Karius and Simon Mignolet. Klopp acknowledged the size of the fee - the most ever paid for a goalkeeper - but felt his club had to act.
The fee beats the previous record for a goalkeeper of 53 million euros paid by Juventus for Gianluigi Buffon in 2001 and the 40 million euros Manchester City forked out to sign Alisson's compatriot Ederson from Benfica a year ago.
"The full package is just good", the coach added.
Jurgen Klopp is thrilled to have signed a "world-class goalkeeper" in the shape of Brazil worldwide Alisson. They were quite excited, so we did it. "We met again in the game when we were up against each other [in the Champions League in April]", Alisson told Liverpoolfc.com.
Undoubtedly a position in need of an upgrade, Alisson is hailed as a player who will bring exactly what the Reds need by most.
Liverpool manager Juergen Klopp says clubs will be "collecting the bones" of overworked players as the worldwide calendar places more demands on teams already struggling to cope with a hectic domestic schedule. They did so behind a remarkable defensive record that saw them concede just 28 league goals, and Alisson's contribution to that can not be denied.
"But of course he still has to adapt and age-wise he can improve, the best years are coming in the goalkeeper life, so it's all good".
That is undeniably true, and fans will soon see just how good their latest signing can be.