Meeson joins from the Legal Services Commission, where she was director of communications.
She started in her new role this week.
Her appointment comes at a time of uncertainty for Monitor, as the Conservatives plan to turn it into a broader economic regulator if they win the general election.
Meeson will be responsible for communicating with health sector partners, Parliament, government, patients and the public.
She said: 'The Conservatives have talked about giving us a broader remit, so there will be a lot of work for Monitor in communicating those changes if they take place.'