According to a club statement on Tuesday, Martino will be given a two-year contract. He will replace Tito Vilanova, who in turn succeeded Pep Guardiola.
Vilanova began as Guardiola's assistant, providing the tactical know-how that helped his then boss forge one of the best teams in the history of the sport — winning 14 of a possible 19 titles from 2008-2012, including two Champions League trophies.
During Vilanova's single season in charge, he led Barcelona to the Spanish league title with a record-tying 100 points. He stepped down as Barcelona coach last week following a recurrence of throat cancer.
Despite having no experience coaching a European club, the 50-year-old Martino received backing from Barcelona star Lionel Messi before the club's sporting director travelled to Buenos Aires to negotiate the deal.
Messi spoke glowingly of Martino, better known in Argentina by the nickname "Tata."
"I like Tata Martino," Messi said recently. "He is a great coach," adding that "his teams play well and we all respect him."
Martino acknowledged Messi's influence in landing the job.
"I have no doubt that Jorge (Messi's father) and Lionel have had importance," Martino said at a news conference in Rosario, Argentina. "They surely have spoken with the club officials. Surely they were asked their opinion."
The club praised Martino on its website for "his clear commitment to the passing game" and the attacking style that have become Barcelona's on-field trademark.
However, in a poll published Tuesday by the Catalan region's leading newspaper, La Vanguardia, under the banner "Do you approve of 'Tata' Martino signing?" 58 per cent of readers answered "no" and only 32 per cent approved. Ten per cent of the 1,000 people polled had no opinion.
Barcelona said it will specify plans for the Argentine's arrival in Barcelona "in the coming hours." Martino is expected to travel from Argentina to sign a contract and be presented officially to the club.
Martino played as a midfielder from 1980-1996, including a short spell in 1991 at Spanish club Tenerife in the Canary Islands. He also led Paraguay to the quarterfinals of the World Cup for the first time, in 2010.
Martino is due to arrive with his assistant from coaching Newell's Old Boys last season, Jorge Pautasso, fitness coach Elvio Paulo Rosso and coach Adrian Coria, who once was in charge of Messi at the Argentine club.
Barcelona says Martino will become the fourth Argentine to coach the club, after Helenio Herrera (1958-60, 1980 and 1980-81), Roque Olsen (1965-67), and Cesar Luis Menotti (1983-84).
Barcelona is due to travel to Germany on Wednesday for a preseason friendly match against Bayern Munich — which is now coached by Guardiola — but Martino is not going to be able to accompany the squad, the club said.
In what he called an "open letter" released Tuesday, Vilanova said his doctors had advised him to give up coaching, but said he would not be leaving the club altogether.
"I will continue to be very close and will carry on working at this club that I love so much on other tasks within the area of sports," said Vilanova without specifying any further.