Having personally invested a substantial undisclosed sum in the three-strong pub chain, Johnson is set to become chairman.
His backing is expected to help the Draft House expand at an increased rate in central London locations.
McVeigh, who had hoped to open the Draft House’s fourth venue by early 2011, said he was ‘very excited’ by the prospect of Johnson’s involvement.
“Clearly his ability to build businesses and do deals in our sector is unparalleled and we are already starting to feel the benefit of his involvement in site selection as well as landlord and bank relations.
“It's also a great vote of faith in a business which our team have worked so hard to build up. We are hoping to be able to announce a couple of site acquisitions in the coming weeks.”
McVeigh currently operates Draft Houses in Clapham, Battersea and Tower Bridge, and is currently close to signing off a fourth and fifth site in undisclosed locations in central London.
Earlier this year he told BigHospitality the group had plans to expand to 10 sites by 2014.
Johnson also has a stake in Ego and Rocket merger 3Sixty Restaurants and Feng Sushi. He has further stakes in Giraffe, Patisserie Valerie and Gail’s Artisan Bakery through investment vehicle Risk Capital Partners.