His wife, Cristina Fernandez de Kirchner, who succeeded him as president, was with him when he died Wednesday, the BBC reported. Within hours, thousands of marchers took to the streets of Buenos Aires to mourn his passing.
Kirchner, who was president from 2003 to 2007, had heart surgery last month.
Officials declared a three-day national mourning period.
Kirchner was lying in state at Casa Rosada, the government palace in Buenos Aires. A funeral is scheduled this weekend.
"A great patriot has gone, a great Latin American," said Rafael Correa, president of Ecuador.
"The best homage we can pay to Nestor is to reiterate our commitment to build this great country, this united America that he dreamed so much of and fought hard for," Correa said.
Venezuelan President Hugo Chavez arrived in Buenos Aires Thursday evening, and told reporters "a just and brave man has died."