A spokesperson for AAPT was unable to respond to iTnews at the time of publication.
But in a statement, the service provider said that its three LiveNet Unlimited plans provide unlimited off-peak downloads between 2am and 8am AEST daily.
The plans start at $49.95, which includes a 20GB peak download limit. If this is breached, speeds are throttled.
There is also a 30GB plan for $69.95 and a 60GB plan for $99.95.
AAPT has previously announced that uploads aren't counted in the peak quotas either.
Existing customers are able to change to the new plans without incurring excess fees, although they will have to restart their 24-month contract period.
A spokesperson for AAPT had previously advised iTnews that details of plans - which were first leaked to Whirlpool - could be several months away.
Details of the plans were again leaked to Whirlpool prior to today's formal announcement.