Martino, who won the Argentine league title with Newell's Old Boys in June 2013 before taking the reins at Barca, will make his debut in a September 3 friendly against Germany in Duesseldorf.
The Germans beat Argentina 1-0 after extra-time in the World Cup final at Rio de Janeiro's Maracana on July 13, after which Sabella decided against accepting the offer of a new contract from late AFA President Julio Grondona.
"The Rosario-born coach Gerardo Daniel Martino will take office as the new coach of the national team, succeeding Mr Alejandro Sabella, who completed his contract with the AFA after the end of the World Cup Brazil 2014," the Argentine FA said on its official website.
Martino was enjoying the early days of a sabbatical after a disappointing season at Barcelona where he took the job left vacant when Tito Vilanova stepped down to undergo cancer treatment. Vilanova died in April at the age of 45.
He got off to a good start at Barca but injuries to key players, including hamstring problems for Lionel Messi, saw the side stutter through the season and he resigned after the club failed to win a major trophy for the first time in six years.
His failure with Barca did not seem to damage his reputation in Argentina, where he is still highly regarded after having a successful club coaching career in Paraguay before returning to Rosario to steer Newell's Old Boys to the league title in 2013.
After hearing from Sabella that he did not want to carry on, Grondona had planned to meet with the 51-year-old Martino to offer him the job.
However, Grondona died of heart failure on July 30.
AFA Vice President Luis Segura took charge and the matter of appointing a new coach was postponed for more than a week.
Despite being critical about how the AFA was run a year ago, Grondona favoured Martino's appointment because he had worked with Argentina captain Messi, also a Rosario native, and midfielder Javier Mascherano at Barca.
A disciple of Marcelo Bielsa, who coached him at Newell's Old Boys, Martino preaches a possession game with thrusting midfield play supporting quick forwards.
His Argentina side could look more like the one Sabella steered through the World Cup qualifiers with a four-pronged attack than the more tactical team he coaxed through to the final in Brazil.
Martino has previous national team experience having taken Paraguay to the World Cup quarter-finals for the first time in South Africa in 2010 and the Copa America final a year later in his home country.
Martino, whose contract will run until the 2018 World Cup in Russia, will be officially presented to the media on Thursday.
- Sports & Recreation
- Alejandro Sabella