The deputy prime minister has upheld an inspector's report that recommended the LDA-masterplanned scheme - which will include 1,250 new homes - should get the go ahead.
The site is part of the ODPM's Milton Keynes Growth Area, and therefore forms part of the Sustainable Communities Plan.
The scheme will not demolish the massive listed 1917 hangars but will ensure that the hugely popular historic structures will have an entirely new context.
The hangars were designed originally by AJ Main, then added to by the Cleveland Bridge Company at a later date.
In his decision letter, John Prescott argued that the scheme would meet 'important national and local plan policies on a brownfield site specifically allocated for housing in the Bedford Borough Local Plan'.
Prescott also pointed out that the scheme would assist in meeting housing need in the borough and the wider Milton Keynes and South Midlands sub-region.