Pinera, 60, is one of Chile's richest men according to Forbes magazine, having made money via a credit cards business and an airline.
Alvaro Uribe, Alan Garcia and Evo Morales, the presidents of Colombia, Peru and Bolivia respectively, were among those who arrived in Chile on Wednesday for the ceremony, which is expected to be sombre due to the recent disaster.
"We would like to deepen our trust because when there is trust, we can solve social problems, and problems such as this earthquake," Morales, who presents a leftist ideology, said.
Michelle Bachelet, the outgoing president, leaves office with an 84 per cent approval rating in Latin America's second biggest economy.
This despite a poll by El Mercurio, a local conservative newspaper, showing that 72 per cent of people believe that Santiago reacted too slowly to the disaster and that 60 per cent of those polled think that aid delivery has been inefficient and not quick enough.
About 14,000 soldiers have been assigned to keep security and assist with the relief efforts and thousands of volunteers have been drafted in to help.
More than 90 per cent of homes in the disaster area are now receiving regular power and warer and food aid is available.
The earthquake did not damage the country's mines - Chile is the world's top copper producer - but important wine, fish and paper pulp industires were seriously affected near the epicentre in south-central Chile.
Some analysts expect losses in such industries to cause national economic growth to drop by half per centage point in 2010.