The Supreme Electoral Council said the former leader has 40.7 percent of the vote, slightly ahead of centre-left rival Otton Solis with 40.3 percent.
The race has been described as the tightest in Central American history.
Costa Rican electoral guidelines say a candidate must gain 40 percent of the vote to avoid a second round run-off poll.
The 1987 Nobel winner previously ruled Costa Rica from 1986 to 1990.
Mr Arias, 65, who is a centrist, was instrumental in mediating in ending a number of bloody Central American conflicts that wracked the region in the 1980s.
He is the candidate for the National Liberation Party (PLN) that advocates a Central American free-trade zone with the United States, and is a coffee and sugar tycoon.
His centre-left rival Otton Solis served as a minister under Mr Arias.
Mr Solis left the PLN in 2000 to protest the party's shift to the right and ran for the presidency in 2002.
However he has rejected the policies of Venezuela's President Hugo Chavez and Cuban leader Fidel Castro, who seek a grand leftist Latin American alliance against the US.
Just hours earlier, an exit poll showed Mr Arias had won with 44.5 percent of the vote.
Low turnout
As expected, voter turnout was low, with only around 65 percent of Costa Rica's 2.5 million registered voters casting their ballot.
The apparent snub is widely believed to stem from disgust over recent political corruption scandals, with two ex-presidents, Rafael Angel Calderon and Miguel Angel Rodriguez, both of the United Social Christian Party (PUSC), charged with taking bribes in 2004.
Calderon is suspected of taking money from a Finnish medical company and Rodriguez from French engineering firm Alcatel.
Both are currently out of prison on bail awaiting their trial but the impact on the PUSC has been devastating.
The conservative party's candidate, Ricardo Toledo, has garnered only five percent support in polls.
Another ex-president, Jose Maria Figueres, of the PLN, is also facing accusations that he took money from Alcatel, and he is refusing to give evidence in Congress.
The corruption storm has overshadowed the real debate for Costa Ricans, the country's widespread poverty. There have been few rallies.