Ledesma replaces Daniel Hourcade, who resigned in June after back to back losses at home to Wales left his side with just two wins in 17 games.
The 45-year-old Ledesma played in four World Cups for Argentina between 1999 and 2011 and has coached at French clubs Stade Francais and Montpellier, New South Wales Waratahs and Argentine Super Rugby club Jaguares.
He said he was looking forward to the challenge of lifting Argentine rugby, which has gone downhill since Ledesma helped them to third place in the 2007 World Cup, to their best ever performance.
"I was fortunate to represent my country many times as a player and now I am proud to be the captain of the ship," Ledesma said.
"I am not intimidated (by the role). One must be responsible, ready to make sacrifices and to work. We have a huge challenge ahead."
His first games in charge will be in November when Argentina play three tests away to Ireland, France and Scotland.
(Reporting by Ramiro Scandolo, Writing by Andrew Downie, Editing by William Maclean)
