The opposition Democratic Unity coalition won 99 seats to the Socialists' 46 in the 167-national National Assembly, the election board said, with some districts still to be counted.
Fireworks were set off in celebration in pro-opposition districts of Caracas when the results were announced, while government supporters dismantled planned victory parties.
Maduro, 53, quickly acknowledged the defeat, the worst for the ruling "Chavismo" movement since its founder Hugo Chavez took power in 1999.
"We are here, with morals and ethics, to recognize these adverse results," Maduro said in a speech to the nation, although he blamed his defeat on a campaign by business leaders and other opponents to sabotage the economy.
"The economic war has triumphed today," Maduro said.
His quick acceptance of the results eased tensions in the volatile nation where the last presidential election in 2013, narrowly won by Maduro, was bitterly disputed and anti-government protests last year led to 43 deaths.
Opposition leaders, who have lost over-and-over since Chavez's first election victory 17 years ago, were jubilant, even though their victory was mainly thanks to public disgust at Venezuela's deep economic recession.
"We're going through the worst crisis in our history," coalition head Jesus Torrealba said. "Venezuela wanted a change and that change came ... a new majority expressed itself and sent a clear and resounding message."
Opposition sources predicted that once counting was finalised, they would win as many as 113 seats. That would give them a crucial two-thirds majority needed to shake up institutions such as the courts or election board.
The result could also embolden government foes to seek a recall election against Maduro in 2016 if they garner the nearly 4 million signatures needed to trigger the referendum.
The government's defeat was another blow to Latin America's left following last month's swing to the center-right in Argentina's presidential election. Read more: