The 29-year-old's contract expires this summer and he has been unable to agree an extension with the club.
Sanctions placed on Chelsea by the UK government for owner Roman Abramovich's links to Russia president Vladimir Putin played a role in Rudiger's contract situation.
Chelsea were prepared to make Rudiger the highest paid defender in their history but agent fees proved too much for the European champions given their current situation.
Chelsea are still waiting for a new owner, with the club up for sale.
Speaking to Sky Sports after Chelsea's 1-0 win over West Ham on Sunday, Blues boss Tuchel confirmed: "The situation is that he wants to leave the club. He informed me of this in a private talk.
"We gave everything - me and the club - but we could not fight anymore because of the actions. Without the sanctions we would at least be able to carry on fighting, but our hands are tied. We don't take it personally. It is his decision.
"He is a key figure and will stay that way until the end of the season. But it is disappointing. We will miss him a lot. He gives courage in the dressing room. The kind everyone is afraid of, but the kind to play 50-55 games at an outstanding level. He is a top defender in the last one-and-a-half years for me. We then need to find another solution."
Rudiger has been linked with a move to Real Madrid.
The former Stuttgart defender has made 47 appearances in all competitions this season, scoring five goals.
Rudiger joined Chelsea from AS Roma in the summer of 2017 and has won one FA Cup, the UEFA Champions League, UEFA Super Cup, FIFA Club World Cup and Europa League in his time at the club.
