The award-winning art director said the move into directing was a "natural progression", adding that it satisfied "a nagging ambition".
Mike Stephenson, Moon's co-founder, said Dunn's extensive agency experience would enable him to have a natural rapport with agency creative teams.
At Moon, Dunn will join a stable of three directors - Stephenson, Bruce St Clair, who directed the launch ad for Microsoft Windows, and Lee Donaldson, whose credits include Sony PlayStation, Thomas Cook, Nintendo, The Sun and Kellogg.
Moon was established in 2001 by Stephenson and Linda Peryer, previously a director and senior producer respectively at The Paul Weiland Film Company.
Stephenson began his career as an art director at the then Boase Massimi Pollitt in 1979, moving later to Lowe Howard-Spink, where he built a strong TV reputation.
He said: "I've a lot of time for people coming out of agencies and it's always a good thing that we understand what the creatives need. Steve isn't only famous in advertising but has done enough good work to show us he has an eye for directing."
Dunn, who has already directed spots for Citizen watches, The Observer and The Guardian, has also made a short film, which was shown at last year's Raindance Festival.
His career includes spells as head of art at Leagas Delaney and Lowe as well as as the creative director of Wieden & Kennedy in Portland. He was hired for O&M in 1999 by the then group chairman, Paul Simons. He has been freelancing as well as setting up a vintage furniture business since completing a six-month "gardening leave" period.
Dunn, whose awards haul includes six D&AD silver Pencils and four Campaign Press golds, said: "I'm very excited to join Moon because it's new and exclusive and echoes my ideals of style and creative integrity."