Martino departed Barcelona by mutual consent in May after the Spanish powerhouse missed out on the La Liga title.
The 51-year-old succeeds Alejandro Sabella, who took Argentina to the World Cup final in Brazil, where they lost 1-0 to Germany after extra-time.
Martino has previous experience coaching on the international scene, leading Paraguay from 2007-11 - steering the nation to the World Cup quarter-finals in South Africa in 2010.
Other clubs on Martino's resume include Libertad (twice), Newell's Old Boys, Cerro Porteno and Colon.
Martino will be presented as Argentina's new leader in Ezeiza on Thursday.
Reports are circulating the former Newell's midfielder will also have a significant hand in how the nation's under-age representative sides will look.
