Arias won re-election in February by a razor-thin margin, 20 years after first taking office.
He backs the US-Central American Free Trade Agreement, or Cafta, which Costa Rica's Congress has opposed.
Costa Rica is the only signatory not to have ratified the pact, an important element of Washington's influence in Latin America, where leaders have increasingly challenged US policies.
On Monday, Arias said the country of 4 million people should embrace free trade and not cut itself off from the outside world.
"Taking Costa Rica to isolation from great movements in the world is a reactionary cause and a betrayal of the country's youth," he said in his inaugural address before dignitaries such as Lech Walesa, former Polish president and fellow Nobel laureate, as well as Laura Bush, the US first lady.
Many Costa Ricans fear the trade pact would put their country at a disadvantage against cheaper US agricultural imports.
Arias, 65, served as president from 1986-1990 when Central America was torn apart by civil wars. He won the Nobel Prize in 1987 for his role in brokering an end to the conflicts.
This time around, he lacks a clear mandate after his unexpectedly close win over Otton Solis, a Cafta opponent.
Arias, who was initially expected to win the February 2 race by a landslide, instead squeaked out a 1.12% victory.
That has left him without a legislative majority, and he must cut deals with other parties to pass the trade pact. The Supreme Court has yet to decide whether a simple majority or a two-thirds vote is needed to pass Cafta.
Arias vowed to clean up Costa Rican politics after a series of corruption scandals involving former presidents.
"From today, there will be a clear and inalterable path when it comes to honesty in public functions," he said in the half-empty national stadium.
Outside, several hundred demonstrators marched in opposition to Arias, who critics say has become too close to business interests over the years.