T-Mobile Galaxy S3 owners, we have good news for you today. After so many leaks, it looks like the official Android 4.1.1 Jelly Bean update you have been waiting for so long is finally available to download over-the-air (OTA), although you should be able to upgrade your phone’s firmware via KIES as well.

As you can see in these images, we’re looking at a 334.19MB download for the SGH-T999 Galaxy S3 version, with the update expected to take around 10 minutes to complete. As always, make sure you have a dependable Internet connection and enough battery juice to get you through the process.

In case you were wondering, we’re looking at firmware version J3O03L.T999UVDLJA for T-Mobile’s Galaxy S3 version, so go ahead, check your devices to see whether you have received the update notification.

Our tipster says that his Galaxy S3 was updated at 1:00 PST time  today (November 14) and that he updated it by checking for updates on the handset.

Thanks, Kristopher Q!