Microsoft has begun rolling out the RTM (release to mainstream) version of the Windows 10 Mobile version of the Anniversary Update.
Those with unlocked Windows Phones that support Windows 10 Mobile will be able to get the RTM version, Build 14393.67, starting today. (Those in the Windows Insider program on the Fast Ring already have Build 14393.67.) Carriers are in charge of when they'll release the update to those without unlocked devices.
Microsoft announced the commencement of the mobile rollout on August 16, exactly two weeks after it began rolling out Windows 10 Anniversary Update for PCs and tablets.
From an addendum to Microsoft's August 2 blog post announcing availability of the Anniversary Update for PCs:
"To manually check for the update, on Start, swipe over to the All apps list, then select Settings > Update & security > Phone update > Check for updates.
"Note that availability may vary by manufacturer, model, country or region, mobile operator or service provider, hardware limitations and other factors."
Only a subset of existing Windows Phone devices are eligible for Windows 10 Mobile. Those include: Lumia Icon, 1520, 930, 640, 640XL, 730, 735, 830, 532, 535, 540, 635 1GB, 636 1GB, 638 1GB, 430, 435, BLU Win HD w510u, BLU Win HD LTE x150q, MCJ Madosma Q501 -- plus any newer phones like the Lumia 950 and 950XL which originally shipped with Windows 10 Mobile.
Update: Microsoft also released today the new Skype preview to Windows 10 Mobile Anniversary Update users.