The relationship between an Azure Subscription and Azure AD is not always obvious, but each subscription is tied to to an AAD tenant, this allows for authorization of users in that tenant to undertake operations on that subscription. Sometimes it is necessary to change the tenant a subscription sits under, usually this is either to change the scope of users that can be granted roles in that subscription, delegate permissions for that subscription, or for services like Azure AD Domain Services, which require the subscription to sit under the AAD tenant that contians the AAD DS instance. When this need arises, it can be quite confusing to find correct process to achieve this.
It used to be that changing a tenant could only be done by a support ticket, then when it could be self served it had to be done in the classic portal, which is no longer around, but still shows up in searches for this topic. However as of January 2018 it is now possible to transfer a subscription to a new tenant yourself using the new Azure portal, and the process is pretty easy.
Be aware, before you make any changes, that moving a subscription to a new tenant will remove all RBAC permissions from that sub (as your moving to a new tenant with a new source for your permissions). Make sure you make a note of any permissions you want to re-apply.
The Easy Way
As of January, the easiest way to transfer a sub to a new tenant is to do it your self in the Azure Portal. There is however is a restriction on this, you need to be use an account that has global admin rights in both the tenants (old and new). If you have these rights you can log into the portal, and click on the subscriptions tab, locate the subscription you want to move and on the top bar you will see an option for “change directory”
Click on this and you will be presented with a screen where you can select the tenant you wish to transfer to.
Click OK and the transfer will start. It will only take a couple of seconds to complete in the portal, however I found I needed to wait 5-10 minutes before it showed everything had moved.
The Slightly Harder Way
If you don’t have the rights you need to transfer the sub, then the first thing I would suggest is to find someone who does, but if that is not possible (say no person has rights on both subs), then you can still undertake the transfer another way if you have access to an account that is the current account owner on the subscription. If this is the case you can log into the Azure Account Center – https://account.windowsazure.com and change the owner of the subscription to a user who exists in the tenant you wish to move to. Once you do this the user will receive an email notification and need to accept the transfer.
The process is a bit convoluted, so if you are looking to do this I would recommend following the documentation here.
The Hard Way
If neither of the options above work for you, then you are left with needing to open a support ticket. Assuming you can prove ownership of both source and destination tenant then the support team will be able to make this change for you.