Following the acquisition, Mawhinney has joined Big as creative director to lead its 25-strong creative department. He will report to Big's chief executive and executive creative director, Dylan Bogg.
The deal went through on Tuesday for an undisclosed cash sum. Quorum's only client, Quorn, will move to Big, which is part of The Mission Marketing Group and has clients including WKD and Domino's.
Before founding Quorum, Mawhinney worked as the creative director at the Manchester-based BJL.
Collins, who was formerly the global creative director at Euro RSCG, will work with Big as a creative consultant.
Bogg said: "We look forward to Billy joining our team and helping us to develop the company and achieve the next phase of growth."