The 30 year old defender will sign as a backup and a direct replacement for Kolo Toure.
The Reds decided to release the former Arsenal and Manchester City defender this summer and have sold Martin Skrtel as well. Injuries to Sakho and Gomez has forced Klopp to look for defenders before the season starts.
After the signing of Klavan, Liverpool are expected to sign another centre back this summer.
Klavan has been very reliable for the Bundesliga outfit since joining them a few years ago and will provide excellent depth for Liverpool. He has also been his country’s best player thrice in the last four years.