If you booked your tarrif online or over the phone, AND if you have received your confirmation of contract ("Auftragsbestätigung") less than 14 days ago, then the easiest way to get rid of the contract with Telekom is to revoke the order ("Auftrag widerrufen").

You can do this here: https://www.telekom.de/kontakt/e-mail-kontakt/festnetz/widerruf-eines-telekom-auftrags

But mind you, this will not work if you closed the contract in a physical shop or if the confirmation was received more than 14 days ago.

If it is too late to revoke, or if you signed up in a physical shop, there is no legal ground on which you could just cancel the contract. If you decide to move to a different apartment, German law expects you to take your contact with you and pay for 24 months as agreed between you and Deutsche Telekom.

There is one chance though: If you move to a new apartment and DT is unable to provide the exact same type of service there, with the same speed etc., as in the old department, you can cancel with three months notice.

To make use of this option, you need to request a move according to section 46 TKG ("Paragraf 46 Telekommunikationsgesetz"). You can do this only over the phone. They will try to cross sell you to a different type of connection if your present one cannot be provided at the new location. Make sure you don't agree to that.

If your booked type of service can in fact be provided at your new location, then the above option does not apply. In this case, you're up to good will on the side of DT.