Karius has been with the Turkish Super League club since August 2018 but announced the end of his stay in an Instagram post on Monday, saying "it is a shame it comes to an end like this".
The 26-year-old will return to Anfield having racked up 67 appearances for Besiktas across all competitions.
He reported Besiktas to FIFA last month, the second time he has done so due to a clash with the club over alleged unpaid wages.
Karius' departure ends a stay that had previously been tipped to end in a permanent transfer.
"You should know that I have tried everything to solve this situation without any problems," Karius added in his post, which was accompanied with a video of some of his memorable moments with Besiktas.
"I was very patient for months telling the board over and over again. Same things happened already last year.
"Unfortunately they haven’t tried to solve this situational problem and even refused my suggestion to help by taking a pay cut."
Karius, who joined Liverpool from Mainz in 2016, did express his gratitude to the Besiktas players, coaching staff and supporters.
"It's important to me that you know I really enjoyed playing for this club a lot," he said.
"Besiktas can be proud having such passionate fans behind them always giving amazing support. You always supported me in good and bad times and I will always remember you in the best way!
"Also I want to say thank you to all my team-mates, coaching staff, including all people working for the club. You welcomed me with arms wide open from day one – thank you so much!”