It is expected to take between 20 to 25 hours to get the vessel from its current location to the capital.
A 500-metre exclusion zone is in place around the towage operation for the journey.
Wellington regional harbourmaster Grant Nalder said he expected the ship to arrive at about 11am.
Two port tugs would meet Shiling, help it to berth, and disconnect it from the Skandi Emerald, Nalder said.
“From where it was in Tasman Bay, Wellington was the most practical choice to bring it to. The ship was too big to go into Nelson, especially with no power, and there was no available space in Picton.”
“Obviously we don’t want it here longer than it needs to be to get the repairs done and get under way,” Nalder added.
Anyone wanting to watch the vessel coming in should do so from land, Nalder said.
“If you are on the water, please stay well away.
“It’s a large ship, you’ve got three tugs working with it, we want everyone involved concentrating on their task and not looking to have to avoid other vessels.”
Nalder said a ferry would go into the harbour before Shiling and then there were a couple of hours before any ferries were due to go back out.
“It’s timed so we can do it with minimal disruption.”
Multiple helicopters and a Defence Force Hercules were sent to Shiling’s mayday call. The 294m vessel was drifting in rolling seas.
The 24 crew members had been preparing to abandon ship but ended up staying on board.
Incident controller David Billington said as of 4pm today, Shiling was tracking at between 5 to 6 knots.
“Weather conditions are reasonably stable for the journey too,” he said.
Billington earlier told the Herald that Maritime New Zealand would closely monitor Shiling for the duration of its stay.
“If there are future issues with the vessel, we will manage those if and when they arise.
“The owners of the Skandi Emerald are working closely with the owners of the Shiling about the ongoing support the tug will provide.”
Billington said the owners and insurers were also working to make sure the correct level of support was available so the vessel could transit back to Singapore.
Shiling’s mayday call is the fourth incident involving the ship that New Zealand authorities have dealt with in the past year.