The organisation picked the agency to oversee all PR in the US, Canada, Europe and other relevant markets such as Brazil, Mexico and China, where the destination is becoming more popular.
Andrews won the business after a competitive pitch against more than five US agencies and the account's incumbent, Burson-Marsteller, the firm said.
The travel and luxury specialist agency will execute campaigns showcasing Costa Rica's culture and unique offerings as a tourist destination for the rest of 2013 through 2015.
Andrews will also promote the country as more than an ecotourism destination, for which it is now well-known, with campaigns to attract visitors for business and weddings as well.
The agency had already worked with destinations and hotels in the Caribbean and Central America, including tourist bodies for the islands of Anguilla and Trinidad and Tobago.
It will work in conjunction with the Costa Rican Tourism Board's advertising agency, 22square, which handles most of the brand's social media activity.
B-M first started working with the Costa Rican Tourism Board five years ago, for a 24-month project promoting it as a tourist destination in North America.
The WPP Group agency declined to comment on the account move.