The Anniversary Update for Windows 10 Mobile didn't release at the same time as its PC counterpart, however, Microsoft India sent out tweet on Twitter saying that it will be releasing for Windows 10 Mobile on August 9th. That tweet was later deleted and no further confirmation to any release dates was provided.
Now, we're hearing reports that the planned release date for the Windows 10 Mobile Anniversary Update is indeed August 9th, for non-carrier locked devices, followed by August 16th for carrier devices (via WindowsCentral). These reports are unverified and no official source at Microsoft has publicly stated these dates, so take them with a small pinch of salt. This provides carriers an extra week to test the update, as is the standard protocol for such updates.
Remember - if you're a Windows Insider on the latest build on Windows 10 Mobile, you already have the Anniversary Update and can download apps from the Windows Store that support the latest features for Windows 10.