Greenwood, who has been with the agency for 13 years, takes over the running of the business from partner Larry Franks.
Franks said he wanted to step back from that responsibility, but would still be working with clients.
'I am now retiring to the back benches,' he said. 'Megan has done a formidable job and she will now look after the business operationally, running things day to day.'
Sister agency Beatwax appointed No.1 Traveller's head of experience, Michael Robey, as MD in February, following Tom Johnson's departure.