It looks like Redmond is making good on its promise and has started rolling the feature out today. The unlimited storage will be given to all Office 365 Home, Personal, and University customers.
The following mail was sent to my inbox alongside other users who signed up for the unlimited storage upgrade:
Ask and you shall receive! We have taken you off the waiting list and your Office 365 account now has access to unlimited OneDrive storage.
We added 10 TB of OneDrive storage to your account to get you started during this initial rollout. If you reach your capacity and need additional storage, or have OneDrive questions, just email us here.
The rollout for the unlimited storage will continue over the coming months, but if you don’t want to wait that long and you want to be one of the very first to get more storage, go here.