In the Telegram Settings, tap on your phone number and an info appears.

The info says:

You can change your Telegram number here. Your account and all your cloud data - messages, media, contacts, etc. will be moved to the new number. Important: All your Telegram contacts will get your new number added to their address book, provided they had your old number and you haven't blocked them in Telegram.

The iOS app will return the wrong error when you try to migrate to a new number that is already occupied by an account. It will say 'try again later', but in fact you need to delete the other account in order to proceed. Android handles this correctly.