The role was previously occupied by one of the agency's founders and owners, Ben Dansie, who is now chief executive.
Dansie said: "Sarah has been a vital part of our success over the past few years."
Wood's former role has been filled by Helen Chadderton, who was formerly a project manager at the agency.
Omobono's clients include the Financial Services Authority, Central Office of Information, Legal & General, Miele and Business Link. It is based in Cambridge.