Users will be able to select programmes from the BBC schedules up to seven days before they are broadcast and download them for viewing on their home computer.
The file may be delivered ahead of the scheduled broadcast time but the user won't be able to view the programme before broadcast.
The Trust decided to approve the plans following a 28-day public consultation, which launched on June 30.
It has also asked BBC management to report reach and usage data for pre-booking six months after it launches on the iPlayer so that it can consider the impact of the function.
The Trust said that it has considered the financial implications of the proposal and decided they are not significant and the cost is low.
The BBC's downloading costs are fixed and BBC management considers that it will not incur further downloading costs as a result of introducing the pre-booking function.
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