The Toulon star has been sidelined since suffering a rib injury in the first half of the 13-9 opening game defeat to England.
However Contepomi has declared himself fit to face Scotland - with the Pumas needing to win to keep alive their hopes of reaching the last eight.
"I had a full-on training session today," he said. "This was the day to train myself, have full contact.
"I'm still in a bit of pain, I'm not pain free but it worked well, and hopefully I'll be playing if nothing happens in the next 48 hours.
"I knew it was going to be very tight and I'm lucky it healed quickly."
Contepomi will start in the centres for the clash, with Santiago Fernandez retaining the No.10 jersey after impressing in the thrashing of Romania.
Contepomi's return, though, means Martín Rodriguez returns to full-back, with Lucas Gonzalez Amorosino dropping to the bench.
In the only other change, Julio Farias Cabello starts in the back row ahead of Alejandro Campos.
Argentina go into the game having lost their two-Test series with Scotland at home in 2010 - however coach Santiago Phelan insists those defeats will mean little in Wellington.
"Argentina are well prepared, we have had two-and-a-half months preparing together and that's the difference from over last three or four years," Phelan said. "We know Scotland are also well prepared, and playing good rugby. It will be a tough game."
Argentina: 15 Martín Rodríguez, 14 Gonzalo Camacho, 13 Marcelo Bosch, 12 Felipe Contepomi (capt), 11 Horacio Agulla, 10 Santiago Fernández, 9 Nicolás Vergallo, 8 Juan Martin Fernandez Lobbe, 7 Juan Manuel Leguizamón, 6 Julio Farias Cabello, 5 Patricio Albacete, 4 Manuel Carizza, 3 Juan Figallo, 2 Mario Ledesma, 1 Rodrigo Roncero.Replacements: 16 Agustín Creevy, 17 Martín Scelzo, 18 Mariano Galarza, 19 Genaro Fessia, 20 Alfredo Lalanne, 21 Lucas Gonzalez Amorosino, 22 Juan Jose Imhoff.
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