The Japanese star successfully completed a medical at the club on Wednesday and will join the European champions for £7.25m – his release clause at the Austrian club.
The 24-year-old could make his debut during Liverpool’s FA Cup clash against Everton on January 5 but is ineligible for their Premier League clash against Sheffield United on January 2.
Minamino can play anywhere across the front three as well as an attacking midfielder.
This season, he’s scored nine goals – including one at Anfield during Liverpool’s 4-3 win against Salzburg – and provided 11 assists in 22 matches.
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Minamino spoke of his delight after joining Liverpool, telling the club’s website: “It has been a dream, my dream to become a Liverpool player. And I’m so excited that the moment has come true.
“To play in the Premier League was one of my targets. I think this is the top-class league in the world; I was thinking if my career as a footballer progressed smoothly, someday I would be able to play in the Premier League.
“But I never thought I would be able to play in this team and I’m really happy about it. I’m looking forward to it.”
Following a UEFA rule change last year, Minamino will be eligible to play in the Champions League despite already representing Salzburg in the competition.
The holders face Atletico Madrid in the last-16.
Liverpool value Minamino more than treble his release clause and he will arrive at the perfect time as Jurgen Klopp’s side seek their first-ever Premier League title.
Fabinho is ruled out until the New Year, while midfielder Georginio Wijnaldum went off injured during Saturday’s victory against Watford.
The signing comes on the day Liverpool face Mexican side Monterrey in the Club World Cup semi-final in Qatar.
On Tuesday night, the youngest Liverpool side in history lost 5-0 to Aston Villa in the Carabao Cup.
Klopp has taken a squad of 20 to Qatar to compete in the Club World Cup, with Under 23 manager Neil Critchley in charge of the youthful squad.