The 22-year-old has agreed to join the Merseyside club for an undisclosed fee, thought to be in the region of £4m.
Karius, who kept nine clean sheets in 34 Bundesliga appearances this season, completed his move today after undergoing a medical.
"It's a very good feeling and it's an honour to play for a club like this," Karius told the club's official website. "They have a special history and the fans are amazing here, so I look forward to playing at Anfield.
"I know a lot about the club from watching them on TV. The history, everybody who plays football knows. There 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."
The German keeper will wear the No.1 shirt.