Former Lithuanian President Valdas Adamkus has won a second term, election authorities in the Baltic nation say.
Mr Adamkus is a former US citizen who lost to Mr Paksas in 2003
They said that with 98% of the vote counted, Mr Adamkus polled some 52.1%, while Kazimeira Prunskiene - his only rival in the run-off - had 47.8%.
Ms Prunskiene conceded the race in the early hours of Monday as the Adamkus camp was celebrating the victory.
The elections were called to replace Rolandas Paksas who was impeached in April on corruption charges.
"I will start negotiating with candidates on Monday and shaping up my team," said Mr Adamkus.
The 77-year-old former US citizen was Lithuanian president from 1998-2003 until his shock defeat by Mr Paksas.
The poll was held days after anti-corruption investigators raided offices of four parties, some of which backed Mr Adamkus. The move prompted suspicions that the raids were politically motivated.
Prunskiene thanked voters for their support
Mr Adamkus won the first round of the presidential poll on 14 June, but failed to get the 50% of the vote needed for an outright win.
Hi rival, Ms Prunskiene, 66, was Lithuania's first prime minister after the former Soviet republic declared independence in the early 1990s.
After Mr Paksas' impeachment, Arturas Paulauskas was appointed acting president.
Mr Paksas was impeached for allegedly leaking classified material and giving a Russian businessman citizenship for financial support - charges he denies fervently.