Demetris Christofias, 61, the Communist party leader, and Ioannis Kasoulides, 59, a former foreign minister and leader of the DISY party, will now face off for the presidency.
They both want talks on reuniting the island.
Final results showed Papadopoulos had 31.79 per cent, compared with 33.51 for Kasoulides and 33.29 for Christofias.
Papadopoulos' concession came in a telephone call to Christofias to congratulate him, state-run CyBC television said.
UN plan rejection
Papadopoulos led the Greek Cypriot rejection of a UN reunification blueprint in 2004, and critics charge that he has made no real attempt to break the deadlock since then.
Christofias had then backed Papadopoulos in rejecting the plan, but it later emerged there were key disagreements on tactics.
Cyprus has been split along ethnic lines since 1974 when Turkey invaded the northern part in response to an Athens-engineered coup aimed at uniting the island with Greece.
A Greek Cypriot-led Cyprus represents the island in the bloc, with veto rights over Turkey's admission.
The EU partially suspended Turkey's EU accession talks in 2006 over its refusal to open its ports and airports to Greek Cypriot traffic.