However as their pro-western opponents hold nearly all the other seats, analysts say the Radicals, who favour closer ties with Russia, will struggle to form a coalition.
Election results released
Serbia's state election commission released official results on Thursday evening, confirming the Radical Party's earlier claims of electoral victory.
In the final count, the Radicals won 81 seats, the pro-Western Democrats took 64 and a moderate nationalist coalition led by Vojislav Kostunica, the outgoing prime minister, won 47.
The pro-EU G17 Plus also won 19, while the remainder went to smaller groups and to representatives of ethnic minorities.
According to the constitution the new parliament must be formed within a month of the official election results being published, and a new government must be in place within three months.
The results were published a day before the United Nations is set to unveil the first draft of its plan for the future of Serbia's Kosovo province, whose ethnic Albanian majority wants independence.
The Radical Party is strongly opposed to plans to grant independence to Kosovo - a province that nationalist Serbs regard as an important part of their homeland.