Norway's Frontline has said its damaged LR2 Front Altair was under tow on Saturday away from Iranian waters.
The 110,000-dwt tanker (built 2016) received permission on Friday night from the Iranian navy to sail.
A tug named as Aquila successfully made a connection to the vessel on Saturday morning.
The tanker was set on fire on Thursday in an apparent torpedo attack.
A third tug, Mubarak Challenger, was due to meet the tow later on Saturday.
A team of specialists including a vessel superintendent will embark Front Altair for a full assessment of the condition of the vessel and damage.
"Options are now being considered for a ship-to-ship operation for the safe transfer of cargo," Frontline and manager ITM said.
The 23 crew remain safe and well in Iran, with plans being made for their repatriation "soonest", it added.
