Repair crew supervisors say they expect partial exports to resume early on Monday.
Last week, saboteurs destroyed sections of two lines bringing all of Iraq's Basra Light exports to a halt, depriving the country of its main foreign currency earner.
Pumping into the repaired pipeline will be gradual and could build up to an estimated 700,000 barrels per day (bpd), assuming there are no leaks.
Test runs will help clean up the pipeline from sand and other debris.
The remoteness of the second sabotaged pipeline in the Faw Peninsula have delayed repairs and forecasts for a resumption of pumping have already been missed.
The Iraqi oil ministry has refused to disclose the progress of repairs in order to keep saboteurs guessing.
Oil exports are vital for Iraq to fund reconstruction after three wars in a quarter of a century and over a decade of sanctions.
The two pipelines feed the main Basra terminal, formerly known as Mina al-Bakr, and the smaller Khur al-Amaya terminal.
Iraq was exporting around 1.6 million bpd from the two southern terminals before the latest attack.
Sabotage on northern oil installations earlier this month stopped what amounted to 200,000 bpd of exports through a Turkish port.