Is it about a 24-month contract? Cancellation by telephone is not possible in this case. 
o2 DSL fixed-term contracts can normally only be terminated with a notice period of 3 months to the end of the agreed term or extension period. 
In the event of a move, the availability at the new address will be checked as part of the customer's move order. If the customer is informed in writing by o2 during the execution of his order to move the connection that it is not possible to provide the service at the new address, the customer can terminate the contract with a notice period of 3 months calculated from the date of the move according to the registration certificate. The termination must be made in text form.  

@blablup thanks for your answer. Can you please suggest me how to raise a move order, any email address where I should write?

I recommend to contact o2 customer support. There is also a special number for service in English. 

Hello @Mrinmoy,

welcome to our o2 Community

As i can see, @blablup  was able to give you some helpful tips already. Have you already managed to contact our English support?

If o2 DSL is not available at your new adress according to this availability check you can cancel immediately with the three months term as written above. 

We need a written cancellation then, including a copy of your registration certificate from the Einwohnermeldeamt at your new adress.

You can send it to

Telefónica Germany GmbH & Co. OHG, Kundenbetreuung, 90345 Nürnberg
or via Fax: 01805571766

I have another alternative for you: you also have the possibility to transfer your contract to the new tenant in your old appartment, if he or she is interested. The contract transfer can be carried out online and is charged with 34,99 EUR to the new contract owner.

Please let us know if you have any further questions, we are happy to help you!

Best regards,

Giulia