Following article describe how to move resources between Azure subscriptions.
https://azure.microsoft.com/en-us/documentation/articles/resource-group-move-resources/
However it says that both subscriptions must exist within the same tenant. Apparently that is not the case with my 2 Azure accounts and I didn't know until now that behind the scenes I have a Tenant ID linked to these accounts.
I'm now wondering how to get some of my accounts that I'm using for my company to be linked to a common Tenant ID.
Any ideas?
Updated answer for the new portal (early 2018).
Follow this link: How to associate or add an Azure subscription to Azure Active Directory to associate your subscription with the new tenant (directory).
Once you've done it, you can transfer between subscriptions.