The Japan forward successfully completed his medical at Melwood on Wednesday, and will move to Anfield when the transfer window opens on 1st January.
The 24-year-old was one of the most coveted players in the Austrian club setup, having been linked with top European clubs like AC Milan, Manchester United and Borussia Dortmund.
"It has been a dream, my dream to become a Liverpool player," Minamino said after signing for the Reds.
"To play in the Premier League was one of my targets," the former Cerezo Osaka forward added.
"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."
Minamino played in both Salzburg’s matches against Liverpool in the Champions League group games, scoring in the 4-3 defeat at Anfield in October.
"From those games I learned this team has such a high level of technique and intensity," he said.
"Their football is of such a high level and I did feel that they were the champions of the Champions League. Feeling that, it makes me feel even happier that I can play in this team. I'm really happy to be part of that team.”
"My target is to win the Premier League and the Champions League, and to make good contributions to the team."
Liverpool manager Jurgen Klopp believes Minamino will help strengthen his squad as his men are seeking to win both the Premier League and the Champions League trophy.
"Takumi is a very quick, very clever player - he finds space between the lines," the German coach said.
"He is brave with the ball but also brave without the ball - a proper team player. He makes the best of himself for the benefit of others.”
"His Champions League experience is a big bonus and coming from the club and organisation he does, we know he'll be well coached, used to an elite environment and had all the right experiences."
The Japanese scored nine goals and provided 11 assists in 22 appearances for Red Bull Salzburg this season.
