Regan is the agency's first major hiring since it opened for business this month with the £50 million-billing Tesco as its founding client.
His departure from Nylon follows a rethink about the future of the planning shop.
The agency, a joint venture by Young & Rubicam Brands and Mediaedge:cia, was set up two years ago to challenge operations such as Naked.
Although the Nylon name is being retained, its functions are being absorbed by Mediaedge:cia. Martin Thomas, another of Nylon's founders, quit to join Media Planning Group in December.
At The Red Brick Road, Regan, 43, will work with David Hackworthy, the strategy partner, to spread the communications planning discipline across the planning department.
Regan said: "We are on the verge of some massive changes in communication and we have to be ready for them to exploit the opportunities they will create. However, this is not a land grab that will put us in opposition with our partner agencies."
Regan's 18-year advertising career spans spells at Cogent Elliott and the then Howell Henry Chaldecott Lury. He is a former director of Bullet Media and a founding partner of Michaelides & Bednash.