The man, Leiver Padilla Mendoza, is suspected by Venezuela of masterminding Mr Serra's death.
Mr Padilla has dual Colombian and Venezuelan nationality.
Robert Serra, 27, was found stabbed to death at his home in October alongside his partner, Maria Herrera.
He was the youngest member of the National Assembly and was seen as a rising star in the governing United Socialist Party (PSUV).
Three days of national mourning were declared after his death.
Venezuelan President Nicolas Maduro said Mr Serra's death was political and carried out by Colombian paramilitaries.
He said Mr Serra's bodyguard had confessed to conspiring with a Colombian gang to kill him.
Delays in the extradition of Leiver Padilla Mendoza had caused tensions between Colombia and Venezuela.
The Colombian Supreme Court had sought assurances Mr Padilla would be fairly treated.
In another development, Venezuelan Defence Minister Vladimir Padrino Lopez announced on social media that eight Venezuelan military officers had been convicted of attempting to  initiate a foiled coup attempt against Mr Maduro's government.
President Maduro announced in February that a retired air force general had been arrested and more than 10 other people implicated in a plot to attack the presidential palace and other buildings.
Venezuelan government officials said at the time the officers had been conspiring with the United States - an accusation the US state department called "ludicrous".
The Colombian president, Juan Manuel Santos, has authorised the extradition of a man wanted in Venezuela over the murder of a Caracas politician, Robert Serra, last October.