You never let me walk alone - Karius says goodbye to Liverpool
The goalkeeper made two crucial errors in Liverpool's Champions League final loss to Real Madrid in May, while he also struggled for form during pre-season.
Liverpool subsequently paid a then world-record fee for a goalkeeper to sign Alisson from Roma, with the Brazilian taking over as first choice between the posts.
Karius is now keen to rebuild his reputation in the Turkish Super Lig after making 49 appearances for Jurgen Klopp's side.
"Proud to be part of the famous Besiktas family now," Karius wrote on Twitter.
"Your welcome at the airport yesterday was simply overwhelming! I will give it my all to win with Besiktas.
"A big Thank You goes out to all of the Liverpool fans for the support until now – you indeed never let me walk alone."
Proud to be part of the famous @besiktas family now. Your welcome at the airport yesterday was simply overwhelming! I will give it my all to win with Beşiktaş.
A big Thank You goes out to all of the Liverpool fans for the support until now – you indeed never let me walk alone. pic.twitter.com/Pw1eqrhFuv — Loris Karius (@LorisKarius) August 26, 2018