The 22-year-old is believed to have penned a five-year deal at Anfield, and will provide competition to current first-choice keeper Simon Mignolet.
"It's a very good feeling and it's an honour to play for a club like this," Karius told the Reds' website.
"I know a lot about the club from watching them on TV. The history, everybody who plays football knows. There are a lot of things in my head when I think of this club.
"I spoke to the manager and I had a good feeling afterwards because he told me what he wants to do with the club and with the players.
"It was a good talk with him and after that I was convinced this was the right decision."
Liverpool manager Jurgen Klopp added: "I am delighted we have signed Loris, he has had a fantastic season with Mainz and has developed into a very good goalkeeper since his return to Germany.
"I am really pleased that we were able to move so quickly to get him and that Loris has shown such a desire to come to Liverpool with a lot of other clubs interested in him.
"I know he will add to the quality we have in this position and I look forward to working with him and all our players when we return for pre-season."
Klopp also agreed deals in January for Schalke centre-back Joel Matip and Red Star Belgrade midfielder Marko Grujic to join the Europa League finalists this summer.