The Croatian defender spent six years on Merseyside, winning the Premier League in his final season at the club.
The centre-back also won the Champions League, UEFA Super Cup and Club World Cup in his last 14 months at the club, for whom he made 185 appearances.
"From the first day, I remember when we played with Dortmund against Liverpool in a pre-season friendly and Dejan scored with a header with incredible power.
"That was the image in my mind when I came here and thought about the defenders we had.
"He played super games and scored one of the most important goals of our history, in the 4-3 against Borussia Dortmund.
"A really wonderful moment to share and so many good games, and when he was fit he was very often in the team.
"A great player, great person. He speaks five languages as well.
"Yesterday we said 'Who is now the best friend of Mo? Because they are real besties. We will miss him, he's a model athlete. He has everything you need. But now he goes to Russia."