An official vote count indicated Mr Arias received almost 665,000 votes in the February 5 poll, beating his main rival Otton Solis, an economist opposed to a free-trade agreement with the United States.
The parties of all 14 candidates have three days to file any complaints.
Electoral council president Oscar Fonseca said an official announcement of Mr Arias' victory will however have to wait until several hundred questionable votes are cleared up, most likely by sometime next week.
"Politics is trust, and if Costa Ricans want me back in office it’s because they summed up all the good things and bad things that happened during my presidency and the good things won out," Mr Arias told reporters.
He previously led the country between 1986 and 1990, winning the Nobel Peace Prize in 1987 for spearheading talks that ended civil wars in El Salvador and Nicaragua.
The question of the free-trade deal with the US dominated the presidential campaign debate.
Costa Rica is the only eligible country yet to ratify the deal, with Nicaragua, Guatemala, Honduras, El Salvador and the Dominican Republic already signed up.