Britain's ITV Studios, which owns the series' rights, will co-produce the 26-episode series, with the working title Thunderbirds are Go!
It's set to be broadcast in England on ITV and the UK's CITV Channel in 2015.
The fictional sci-fi series, which revolves around the rescue missions of the five heroic Tracy brothers, will be produced using CGI animation and live-action model sets.
It is currently in pre-production.
Mr Anderson died in December, aged 83.
In a statement, ITV Studios says the series will showcase Pukeko Pictures' and Weta's ground-breaking creative and technical excellence to deliver "a whole new level of action-adventure animation for today's audience, whilst also affectionately paying tribute to the legacy of model locations from the classic series".
"It is thrilling therefore to think we have the opportunity to work with ITV on this new series inspired by this most wonderful of British shows," he said.
"I personally, together with the teams here at Pukeko Pictures and Weta Workshop, look forward to designing and creating an inspirational world that will engage the imagination of a whole new generation as it did for us nearly half a century ago."