The sitcom - which originally aired on ABC between 1969 and 1974 - followed architect Mike (Robert Reed), his new wife Carol (Florence Henderson), his three sons and her three daughters as they formed a single family unit.
The new Brady Bunch has been written by Mike Mariano (My Name Is Earl) and is in development at CBS.
The show will follow Bobby - the youngest Brady child - who now has a 'blended' family of his own with a divorcee and also shares a child with his new wife. Unlike the original series, Bobby and his wife's former partners will also feature.
The Watch star Vaughn originally devised the idea for an update, Deadline reports, and will executive produce with Mariano and Lloyd Schwartz, son of late Brady Bunch creator Sherwood Schwartz.
The original Brady Bunch spawned a number of spinoffs and sequels, including spoof films The Brady Bunch Movie (1995) and A Very Brady Sequel (1996).
The new TV version currently has a script order at CBS.
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Watch title sequences from the original Brady Bunch below: