The 50-year-old Martino, a Rosario native like Barca's World Player of the Year Lionel Messi, has agreed a two-year contract, his new club said on their website.
"The agreement is pending the drafting and signing of the contract," they added.
"In the next few hours, the timetable of his arrival in Barcelona, the signing of the contract and his presentation to the media will be firmed up."
Vilanova, 44, stepped down last week to continue treatment for throat cancer after leading Barca to the La Liga title in his first season since taking over from Pep Guardiola.
Known as "Tata" (grandad), the silver-haired Martino burnished his reputation after steering Messi's old club Newell's Old Boys to Argentina's "Final" championship last month and to the semi-finals of this season's Libertadores Cup.
He made his name as a coach when he took Paraguay to the last eight of the 2010 World Cup, where they lost 1-0 to eventual champions Spain, and after quitting in 2011, turned down a lucrative offer from Colombia.
Martino elected instead to return to Newell's, the club where he played 509 matches as a midfielder under compatriot Marcelo Bielsa, from whom he is said to have inherited many of his coaching ideas.
He is also a self-confessed admirer of Guardiola, who took over at German and European champions Bayern Munich at the end of last season.
"I feel identified with the kind of football Barcelona play," Martino told Spanish sports daily Marca in June.
"It's the style I like most," he added. “The respect for the ball, playing out from the back, possession, interchange of passes. The pass is the essence of football."
Martino becomes the fourth Argentine to coach at Barca after Roque Olsen, Helenio Herrera and Cesar Luis Menotti.
His main priorities next season will be to retain the La Liga title while leading Barca to a third European crown in six seasons and their fifth overall.
He inherits a team which has lost several younger members, including midfielder Thiago Alcantara to Bayern Munich, but has added Brazil forward Neymar, seen as one of the most exciting talents in the game.
Club officials have also said they want to buy another centre back to partner Spain's Gerard Pique and that Paris St Germain's Brazil captain Thiago Silva was their primary target.
Barca launch their bid for a fifth La Liga title in six years at home to Levante on the weekend of August 17-18.