Samsung has begun rolling out the Android 4.1.1 Jelly Bean update to unlocked Samsung Galaxy S III handsets, fulfilling its promise to unhappy customers.

The update is available both via Kies and over-the-air (OTA), though there are reports of queues for the latter. At Pocket-lint, we have successfully installed the update on our own unlocked Samsung Galaxy S III using Kies.

READ: Hands-on: Samsung Galaxy S III Jelly Bean review

The mass rollout comes after both Three and Vodafone made the update available early to customers who had purchased the Samsung Galaxy S III locked to their respective networks. 

Following Three and Vodafone’s announcement, Samsung was quick to inform disgruntled customers that they too would be receiving the Android 4.1.1 Jelly Bean update, though not for a few weeks.

Thankfully, that time has arrived and now those customers who bought the Samsung Galaxy S III unlocked will be able to update their handset to Android 4.1.1 Jelly Bean.

Google is due to host an Android event in New York on 29 October, with rumours that a new updated Android 4.2 Jelly Bean will be unveiled.