The 49-year-old, who ended his four-and-a-half-year tenure with Paraguay after steering them to the Copa America final in July, is a lifelong Newell's fan and spent almost all of his playing career as a midfielder with the team.
"After realising the situation Newell's is going through and analysing everything, what led me to take this decision was to have been convinced [by the offer] and above all to have inner peace," Martino said.
"It's true that with the Colombian [Football] Federation we had an agreement that was practically settled... through their president Luis Bedoya who did all the right and necessary things to contract me," he told a news conference at Newell's Marcelo A. Bielsa stadium.
"I had to decide and I chose this. Faced with two work proposals, a national team and the club that saw my [footballing] birth, I chose the latter," added Martino, who is nicknamed "Tata" (grandad) from the days he was a veteran captaining a team mainly of youngsters.
Martino replaces the sacked Diego Cagna, who was appointed at the end of September midway through the Apertura, the first of two championships in the Argentine season.
Cagna took over at Newell's with the club struggling after one win and six draws from nine matches and failed to reverse their fortunes.
Newell's failed to pick up another victory although they drew another seven games to finish the 19-match championship with 16 points and will need to improve in the Clausura starting in February to avoid the risk of relegation.
When Newell's renamed their stadium at Rosario's Parque Independencia in 2010 after their former coach Bielsa, now at Athletic Bilbao, they also put Martino's name to one of the stands.
Colombia will continue their search for a new coach after sacking Leonel Alvarez earlier this month.
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