Hickey joins from Primus, Group M’s dedicated unit for Johnson & Johnson. She managed the multimillion-pound business in six markets across Northern Europe.
In her new role, Hickey will be responsible for managing client relationships, new business and consultancy.
Hickey replaces Nick Baughan, who was promoted to UK chief executive in October 2014.
Before Primus, Hickey was a managing partner at MEC and the chair of the commercial strategy board.
She began her agency career at the Dentsu Aegis Network-owned Carat.
Baughan said: "Anna has a terrific track record of agency leadership and client services, as well as a proven entrepreneurial spirit.
"She is the epitome of all our values and is absolutely the right person to help us take Maxus into its next phase of growth and development."
Maxus is the seventh-biggest media agency in the UK, with more than 250 staff handling billings in excess of £450 million.
Its portfolio of clients include L’Oréal, BT, Barclays, Fiat, Associated British Foods, Npower and Avis Budget Group.
Hickey said: "I love the team’s ambitious energy and am looking forward to working with a great set of people and a great set of clients."