"The people have judged and decided. Their choice is completely respected," Papadopoulos said in a speech to the Cypriot people.
Communist party leader Demetris Christofias, 61, and 59-year-old former Foreign Minister Ioannis Kasoulides of the right-wing DISY party will now vie for the five-year presidency in next Sunday's runoff.
Papadopoulos, 74, had seen his slim lead in opinion polls eroded in recent weeks, but he had been widely expected to advance to the second round.
The vote had been billed as a verdict on center-right Papadopoulos and his handling of the island's 34-year division. The president was instrumental in successfully urging Greek Cypriots to reject a U.N. reunification plan in 2004 which the Turkish Cypriots approved in referendums.
Final results showed Papadopoulos had 31.79 percent, compared with 33.51 for Kasoulides and 33.29 for Christofias.
Kasoulides defied early projections which had him trailing his two rivals despite closing the gap in the weeks before the election. Now, voters drawn from the pool of Papadopoulos supporters are likely to determine the winner in the runoff.
DISY leader Nicos Anastasiades called for unity, saying that although his party disagreed with how Papadopoulos handled national issues, "we never denied his patriotism."
"We now call upon Tassos Papadopoulos and his supporters to join with us," he said. "There are no winners or losers in this election ... this is not a time for winners' arrogance."
Supporters of both Christofias and Kasoulides spilled out onto the streets of Nicosia, cheering, honking car horns and waving Cypriot and a few Greek flags.
It was the first time since Cyprus gained independence from Britain in 1960 that there had been three, rather than two, top contenders for president.
All three claimed to be best qualified to head negotiations with the Turkish Cypriot community, separated from the Greek south since 1974 when a failed bid to unite the island with Greece triggered a Turkish invasion.
Each promised to clinch a new reunification agreement more attuned to Greek Cypriot concerns, but Christofias and Kasoulides argued the stakes are too high for a reprisal of Papadopoulos policies that have driven the island closer to permanent partition.
Cyprus is internationally represented by the Greek Cypriot government in the south, while the breakaway Turkish Cypriot north is recognized only by Ankara.
Despite Turkish Cypriot approval of the 2004 U.N. plan, its rejection by Greek Cypriots in separate referendums meant the island joined the European Union that year still divided.
Some 516,000 voters, including 390 Turkish Cypriots, were registered to vote. Voter turnout was more than 89 percent, election authorities said. Voting is compulsory in Cyprus.