The officials say the pumping started Thursday morning. Around 20,000 barrels are being pumped per hour.
The officials spoke on condition of anonymity as they were not authorized to make statements before the official announcement.
The new terminal is the first of five that will eventually handle about 5 million barrels a day. The terminal is intended to eventually handle 900,000 barrels a day.
The new export capacity will help Iraq to bring in sorely needed cash for reconstruction after decades of war and international sanctions.