Acting Senior Sergeant Craig Madden said the truck rolled near the roundabout's Maungatapu exit at 8.40am.
It had just come through the Welcome Bay roundabout and was heading toward Te Maunga.
McLeod Cranes operations manager Dean Wright said it was the first incident of its type that he could recall at the roundabout.
He said the longest part of clearing the site was cleaning the mess out of the bin. That was done by a mini-digger and front-end loaders brought in by Page Earthworks, with another truck used to cart away the rubbish.
Mr Wright said a front-end loader slid the bin forward to free the bin from the truck and the crane lifted the truck back on to its wheels. Rowe Motors workers then went under the truck and used a big winch to take the truck away.
"We righted the bin and lifted it on to another truck. There was no drama," Mr Wright said.
He would not speculate on the cause of the incident.
Mr Madden said the crash was being investigated by the Commercial Vehicle Investigation unit to determine whether any charges would be laid.