Links from the port, Stanley St and Wellesley St to the Northern and Northwestern motorways were expected to re-open about 2.30pm.
An eyewitness said it was astonishing the driver wasn't killed this morning.
"I thought he was dead. I thought I was going to see something pretty horrific."
The motorist was only moments away from colliding with the truck.
"It was frightening. It happened right in front of me," he added.
Police said the truck driver had a "very lucky escape" and only sustained minor injuries.
The NZTA said crews cleaned the motorway, blocked drains to prevent pollution entering, and would have to re-patch the port link section of motorway where the truck had "gouged into the road".
A lane on the Southern Motorway was also closed to repair the broken barrier.
The bank the truck plunged down was also inspected for possible damage.
A crane removed the truck from the motorway shortly before noon.
Regal Haulage company director Brett McHardie credited the Volvo truck's safety features for the driver's amazing escape.
Mr McHardie said the truckie was "a very experienced driver" and was on his way to Northland when the crash happened.
The driver was familiar with the route and had been a truckie for at least the last 10 years.
"It's a great result for what could've been a horrible situation," Mr McHardie said. "He's doing really well."
