After agreeing terms and passing a medical, the 22-year-old put pen-to-paper to make his switch from FSV Mainz 05 official but will not be on the Reds' books until July 1, when the summer transfer window opens.
Having had his request to wear the No.1 shirt by Klopp granted, Karius becomes the second signing of the summer and the third under the German's helm, following Joël Matip and Marko Grujić with the three only costing a combined £9.8 million.
The Germany Under-21 international will bolster the club's options between the sticks for the 2016-17 season, providing much-needed strength in depth alongside Simon Mignolet, and Klopp believes he has the quality to become an asset to the side straight away.
Reds boss pleased Karius has turned down other clubs to sign for Liverpool
Speaking to the club's official website, Klopp declared himself "delighted" to have signed Karius, insisting that he had "a fantastic with Mainz" which has allowed him to develop into "a very good goalkeeper since his return to Germany."
The Reds boss further said that he is "really pleased" that Liverpool "were able to move so quickly" to sign the shot-stopper and also that Karius has "shown such a desire to come to Liverpool" given that "a lot of other clubs [were] interested in him."
Karius, who admitted that speaking with Klopp convinced him Merseyside was the right destination to pick, spent two years as a teenager in Manchester City's Academy and the German manager believes he will "add to the quality we have in this position" and said: "I look forward to working with him and all our players when we return for pre-season."
Klopp will now press ahead with plans to recruit throughout the rest of his squad, with Leicester City left-back Ben Chilwell and midfielder Mahmoud Dahoud of Borussia Mönchengladbach both thought to be high up his list.