Supporters of the former leader also plan to launch a congress bill blocking any moves to put the general on trial.
Speaking after the ruling, President Lagos appealed for calm, saying the world would be watching Chile closely at this time.
The decision effectively opens the way for charges to be brought against the 84-year-old general relating to alleged human rights abuses during his regime.
Campaigners celebrated in the streets as the news reached them, but General Pinochet's supporters said they would stage protests later on Tuesday.
Supporters of the former leader also plan to launch a congress bill blocking any moves to put the general on trial.
General Pinochet's family remained defiant after the ruling, which his younger son Marco Antonio attacked as a ''political process."
"If any trial takes place, my father will almost certainly not see its end, but I will fight all the way," he said.
The general also remains a popular figure among the Chilean military. Four armed forces chiefs visited the general at his home following the court announcement.
Verdict welcomed
Several countries, including France and the United States have already warmly welcomed the move.
French Prime Minister Lionel Jospin said he hoped the verdict would allow those who lost relatives and friends during the Pinochet era to finally obtain justice.
US State Department spokesman Richard Boucher called the ruling 'historic', and human rights group Amnesty International said the decision was a 'victory for Chilean Justice.'
Next stage
A BBC correspondent says attention in Chile is now focusing on the next stage of the legal process.
According to Chilean law, investigating magistrate Juan Guzman must order medical tests to be carried out on Augusto Pinochet to determine whether he is fit to stand trial.
Lawyers representing the ageing general are expected to seek to prove that he is unfit to stand trial, by demonstrating he lacks the mental capacity to deal with the situation.
Under Chilean law, only mental incapacity - and not physical illness - is seen as grounds for avoiding trial. Observers believe the legal obstacles could still delay any trial for years.
Despite this, many campaigners, some of whom lost relatives during the Pinochet regime, have greeted the decision as a significant step forward.
"This is a very emotional moment. We dedicate it to the many victims of repression under Pinochet," said anti-Pinochet lawyer Eduardo Contreras.
'Caravan of death'
General Pinochet's enemies have spent years trying force him to answer charges of alleged human rights abuses during to his 1973-1990 regime.
More than 3,000 people died or disappeared after General Pinochet took power in a military coup in 1973.
Central to the case against the general are the allegations of his involvement in the "Caravan of Death".
The military squad roamed Chile in October 1973 and is believed to have killed at least 72 people, mainly dissidents dragged from prisons and summarily executed.