Ibrahima Konate joined from RB Leipzig for £36m
Konate, 22, made an overall 21 appearances for Leipzig this season including eight Bundesliga starts as the club finished second, 13 points behind champions Bayern Munich.
He will begin a long-term contract from July 1, subject to international clearance and a successful work permit application process.
"I'm really happy to be joining such a massive club like Liverpool," Konate said.
"It's a really exciting moment for me and my family and I am really looking forward to meeting my new team-mates, the staff and getting started on this new chapter."
Konate, who is currently with France preparing for the UEFA U21 European Championships, will now become the club's first confirmed signing of the summer.
"I’m really pleased we’ve been able to add a player of Ibrahima’s quality to our squad and he is someone I’ve admired for a long time, ever since I first became aware of his potential when he was at Sochaux,” Klopp told Liverpoolfc.com.
"After the problems we had with injuries in the centre-half position last season, there’s no doubt it was clear it was an area of the team we needed to strengthen – but I first have to say that the job Nat, Rhys and Ozan did was incredible. Unbelievable really.
"In Ibrahima we are signing a player who will add to the quality we already have here. His physical attributes are very impressive; he is quick, he is very strong and he is dominant in the air.
"He comes to us after playing more than 90 times for Leipzig in the Bundesliga and European football. I’m sure that number would have been more but for some injury, but even so that means he already has experience of what it takes to compete in two outstandingly difficult competitions.
"He also played for a team in the Champions League in high-pressure matches, who have a similar football vision to ourselves.
"I am confident we are signing a player who can play for us right away, but he is a boy of 22 years of age who has room to improve because of his massive potential. I know that’s something he is eager to work on with us to become an even better player.
"For me, that’s really exciting because I have seen how good he is already and I’m looking forward to working with him when he joins up with us in pre-season."