The National Election Office on Sunday projected the Socialists and their coalition partners winning 210 of the 386 seats in the legislature, 12 more than they hold now.
The two centre-right opposition groups were seen winning 175 seats, with one seat going to an independent candidate.
Official results in 11 districts where the margin of victory was very small were expected to be announced in a few days - after the ballots from Hungarians voting abroad were counted - but they were not likely to affect the coalition's success.
Laszlo Solyom, the president, said that once the results were final, he would initiate talks with the parties in parliament to form a new government as soon as possible.
"I want to give thanks to all the citizens who exercised their right to vote," Solyom said.
Gyurcsany, who arrived at Socialist Party headquarters about an hour before voting stations closed at 1700 GMT, was last among leaders of the main parties to speak once the outcome seemed certain.
"We have won!," a beaming Gyurcsany said, before quickly adopting a more serious tone by saying that electoral victory was not about power, but about responsibility and tasks.
"We have won responsibility for the interests of 10 million Hungarians and responsibility in the name of 15 million Hungarians," Gyurcsany said referring to those living outside the country, including some 2.4 million ethnic kin in neighbouring countries.
The Socialists and their partners
are projected to win 210 seats
With ballots from 98.3% of voting districts counted, voter turnout was 64.3%, compared with 67.8% in the first round, the National Election Office said.
Viktor Orban, leader of Fidesz-Hungarian Civic Union, the main centre-right opposition party, was quick to concede defeat and faulted the lack of unity among the conservative parties.
"Those who unite win, while those unable to join forces always lose," Orban said, a clear reference to the Hungarian Democratic Forum, or MDF, which Fidesz unsuccessfully tried to woo between the two rounds of voting.
Led by chairwoman Ibolya David, the MDF - which was part of the Orban-led government in 1998-2002 but since has tried to come out from under Fidesz's shadow - exceeded expectations by getting just over 5% of the vote and securing its place in parliament.
The next government faces a tough challenge posed by a huge budget deficit - the largest in the European Union compared to the size of the economy - and mounting pressure from the EU for economic reforms paving the way for adopting the euro.
Gyurcsany, 44, initially came to power in September 2004, after Peter Medgyessy was forced from the prime minister's office by the coalition parties, concerned about his lack of leadership and the government's unpopularity.
The opposition Fidesz-Hungarian
Civic Union has conceded defeat
A communist youth leader in the 1980s who later became one of Hungary's richest businessmen, Gyurcsany has vowed to implement structural reforms and get Hungary ready to adopt the euro in 2010.
In September, Hungary must show the European Union the blueprint it intends to follow in switching to the euro. After already postponing its original euro target date of 2008, further delays could undermine confidence in the Hungarian economy.