True to their word, AT&T has announced that the Windows Phone 8.1/Lumia Cyan, which they said would be released as soon as this week, is now available to download for the Nokia Lumia 1520.
Starting at 1PM ET today, AT&T has announced that the Lumia 1520 is cleared to receive the Windows Phone 8.1 and Lumia Cyan update. AT&T did not comment on timelines for their other Lumia phones, though presumably they are not too far behind the Lumia 1520.
To see see if the update is available for your handset, go to Settings > Phone Update and Check for Updates.
P.S.- WPCentral notes that if you have Windows Phone 8.1 Developers Preview installed then you need to downgrade before you can get the Lumia Cyan update.