Alisson was yet to make his Serie A debut when Salah joined Liverpool for €42m last summer, but over the last 12 months he has come to be rated among the top goalkeepers in European football.
Liverpool's new signing, who described the move as "a dream come true", revealed that Salah had impatiently texted him on the eve of the announcement.
"Yesterday, he sent me a message saying: 'Hey, what are you waiting for?'" Alisson told Liverpoolfc.com on Thursday.
"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's rise to becoming one of the world's top-rated goalkeepers over the last year has been mirrored by Salah's ascent to being regarded as the Premier League's top marksman.
His 32 league goals last season set a new record for a 38-game season as he became the first Liverpool player since Luis Suarez to win the golden boot.
He scored 44 goals in all competitions, two of which came against Alisson when Liverpool blitzed Roma 5-2 at Anfield in the Champions League semi finals.
With Salah having agreed a new five-year contract earlier this summer, Liverpool fans can hopefully look forward to many years of Salah and Alisson playing alongside each other.