Velez said on their website that Gareca, known as the Tiger during his playing days, would replace Hugo Tocalli, whose contract was not renewed.
Tocalli led Velez to a ninth-place finish in the Apertura championship, which ended on Sunday -- apart from the title playoff.
Gareca, previously coach of Peruvian side Universitario, is famous for scoring a last-gasp goal which earned Argentina a 2-2 draw at home to Peru and allowed them to qualify for the 1986 World Cup, which they went on to win.
However, Gareca was not called up for the finals in Mexico by coach Carlos Bilardo.
He played for Colombian side America, helping them reach successive Libertadores Cup finals which they lost, as well as River Plate, Velez and Independiente in his homeland.
His coaching career has taken him to America and Santa Fe in Colombia and Argentine clubs Talleres, San Martin-Tucuman, Independiente and Argentinos Juniors.
Gamboa told reporters that he had decided to leave Rosario-based Newell's after club president Eduardo Lopez, who had hired him, failed to be re-elected on Sunday.
The former international defender had been in charge since August and led Newell's to a fifth-place finish.
"I'm not continuing," he said. "I don't want to betray anyone. With great pain in my soul, I have to leave the club."
‘We were in Amsterdam, so I faked a toothache to go and see Crystal Palace in the FA Cup final. I couldn’t make the replay, though – the Stones worked it out’: Rolling Stones guitarist Bill Wyman feigned injury to watch 3-3 draw with Manchester United
‘Home truths needed to be spoken at Manchester United and Ruben Amorim has been brave enough to do that – the way he’s dealt with Marcus Rashford has been correct’ Former Red Devils star praises new boss
