Goalkeeper Karius terminated a two-year loan spell with Turkish giant Besiktas in May due to a disagreement over the payment of his wages.
The 27-year-old, who joined Besiktas in August 2018, on Monday sealed a returned to his homeland.
Karius arrived at Anfield from Mainz 05 in 2016 and played 49 games for the Premier League champions, but was dropped after making some embarrassing mistakes, including on the 2018 Champions League final.
He had been tipped to complete a permanent move to Besiktas, where he made 67 appearances in all competition.
Karius' Liverpool contract expires next June.