Work will begin on Monday (1 August) after a competitive pitch process involving four agencies.
The brief had been held by former lastminute.com PR director Louise Prior's agency Prior PR, who was first appointed in 2011. Prior was among agencies pitching for the new brief.
The key focus of Four's work is to increase the profile and grow bookings for both brands.
The account will be headed up by Four creative director Lalla Dutt, who said: "With seismic shifts in the way people choose and book their travel experiences, this is a truly exciting time to be working with such innovative brands with interesting history and heritage."
Other Four Travel accounts include the Costa Rica Tourism Board, Greater Miami Convention & Visitors Bureau and The Beaches of Fort Myers & Sanibel, a local tourism board in Florida.
STA was created in 1979, and it launched Bridge the World in 2010. It now has more than 2,000 staff in 11 countries, and carries more than 2.5 million passengers annually. Global turnover exceeds $1.2bn (£910m).
STA also works with student marketing agency Campus Group in the UK.