A man and a woman were held at 8.30pm local time on Tuesday after arriving on a flight into the London airport.
The pair, both 26, were arrested by officers from the Metropolitan Police's Counter Terrorism Command on suspicion of the commission, preparation or instigation of acts of terrorism, PA reports.
They were taken to a central London police station where they remain in custody.
The arrests are part of an investigation into travel to Syria in support of alleged terrorist activity.
Officers are searching two addresses in east London under the Terrorism Act in connection with their inquiries.