The former Barcelona head coach is to be officially presented as Alejandro Sabella's successor on Thursday
Martino had long been expected to take over the national team following the departure of Alejandro Sabella, who opted to step down after losing the World Cup final to Germany.
The 51-year-old is set to be announced as the new Albiceleste boss at an official unveiling on Thursday, with the AFA having delayed the proceedings initially following the death of president Julio Grondona on July 30.
Speaking to TyC Sports, Lemme explained there had been "no problems" over a deal with Martino and that he would be presented to the press this week, with the AFA later confirming the news via a statement on their official website.
Martino's deal is expected to last until the conclusion of the qualifying campaign for World Cup 2018, with an automatic renewal triggered should Argentina reach the finals in Russia.
The former Newell's Old Boys boss is expected to oversee the entire structure of the national team set-up, including the youth levels, as he prepares for his first major test with the senior side - the 2015 Copa America.