The protests were mostly peaceful, although there were clashes around the plaza after police tried to disperse protesters with tear gas and water-launch trucks, as the latter responded by throwing stones.
It has been changed before by referendum, following a 1988 vote that paved the way for a return to democracy.
The President called on lawmakers to work on passing a series of reforms aimed at meeting protesters' demands, including raising the minimum wage.
"Leave behind all these feelings of conflict, of division, of confrontation and look for what unites us, instead of looking for what sets us apart," he added.
Pinera signed the enactment at the presidential palace in the company of socialist former president Ricardo Lagos, who 15 years ago introduced a number of significant constitutional reforms.
