Canvas, which counts the BBC, ITV, Channel 4, Five, Arqiva, TalkTalk and BT as it members, aims to upgrade the Freeview and Freesat platforms to support video on-demand and internet services.
Over the last year, the Trust has conducted a "rigorous and extensive period of consultation" on Canvas to gauge its market impact and value to licence fee payers.
After provisionally approving the project in December last year, the Trust has now given the final greenlight for the BBC to be involved in the venture going forward.
However, it has placed a number of conditions on the project, chiefly that it must effectively engage with the wider industry as the new platform is being developed.
The Canvas partners now have 20 working days to publish all completed elements of the platform's core technical specifications. All final specifications must then be released "no later than eight months before launch of the first set top boxes".
The Trust said that Canvas must be made available free-to-air, but providers should also be able to offer paid-for services on the platform, such as video on-demand.
Crucially, the Trust said that entry to the platform must be made available to all content providers and internet service providers.
Entry controls to the platform must be "minimal" and access should "not be bundled with other products or services", said the Trust.
Listing on the Canvas user interface must also be "awarded in a fair, reasonable and non-discriminatory manner" and there must be a "minimum level" set for quality standards for all ISPs supporting Canvas.
The BBC has been warned that it must not exceed its estimated costs for the project by more than 20% over a five-year period. The corporation must also comply with all laws pertaining to competition and state-funded enterprises.
The Trust said that it delayed its final decision on Canvas until the Office Of Fair Trading had completed its assessment of the project, which indicated that the venture does not constitute a qualifying merger.
"The Trust has concluded that Project Canvas will deliver significant public value for licence fee payers - people with a broadband connection will be able to access a wide range of on-demand content including BBC iPlayer, free of charge, through their TV sets," said BBC trustee Diane Coyle.
"We have however applied a number of conditions to the BBC's involvement in the venture in recognition of the potential impacts on the market if Canvas is successful."
The Trust will continue to review the BBC's involvement in Canvas against the conditions it has set for up to 12 months after the platform launches to consumers.