The project had been beset by delays, with Kurdish officials locked in dispute with the central government in Baghdad over how to distribute the country's oil revenues.
Baghdad has for months called the Kurdish move to export oil illegal because the deal was struck independently of the central government.
But Al Jazeera's correspondent Hoda Abdel Hamid said the government has now"quietly given the Kurds the green light for these oil exports", essentially because it needs the money the commodity will bring.
"Total projected oil revenues for the year could be as high as $36.5bn, but not enough to cover the government's day-to-day expenses," she said.
"Kurdish exports could soon reach 250,000 barrels per day worth $15m - a boon for the Iraqi government."
The Kurds are set to get 17 per cent of the oil revenue, equal to their estimated share of the overall population, while Baghdad will get the remainder.
Initial exports are estimated to be around 40,000 barrels a day from Taq Taq, but a Kurdish government spokesman said officials expect the level to reach 250,000 barrels a day by the middle of next year.