The aerial application of 1080 across 22,000 hectares of forest in late 2018 was conducted by the council in partnership with the Department of Conservation.
Both figures represented an all-time low for predator populations in the area.
The drop was undertaken to protect the ranges' native species, particularly the kōkako, which faces an "immediate high risk of extinction" according to the Department of Conservation.
Auckland Mayor Phil Goff said the latest pest control operation was evidence of huge progress being made towards a predator-free Auckland.
"We have to eliminate predators to allow our bush and our native birds to regenerate. The impact in the Hunua Ranges in wiping out rats and possums has been impressive and allows our native birds and trees to recover," he said.
"We can see the results in the doubling of the number of kōkako breeding pairs, meaning we now have the fifth largest kōkako population in the country in the Ranges, reducing the risk of extinction of this and our other precious native bird species."
In 1994, only one breeding pair of kōkako remained in the Hunua Ranges.
At the end of 2018, a census carried out within the Kōkako Management Area counted 106 pairs, nearly double the 55 pairs that were counted in 2014.
The council's environment and community committee chair Penny Hulse said pest control in the Hunua Ranges was responsible for the resurgence of the kōkako population within the forest.
"This shows how effective pest control can save a unique species from near extinction. This is why we must continue to do it," she said.
"The kōkako are now here for future generations as a unique part of the Hunua ecosystems.
"We have also recorded our best fledgling result from our six monitored pairs with 18 chicks fledged. These are remarkable results that are a direct credit to the hard work put in over the last 24 years."
An earlier 1080 drop was undertaken in 2015.
However, possum and rat numbers increased in the following years as a result of reinvasion from untreated areas.
The treatment area for the aerial application of 1080 bait was expanded in 2018 as a result of the recently introduced Natural Environment Targeted Rate.
Department of Conservation Auckland operations director Andrew Baucke said 1080 remained the best way of addressing the risk of predators to New Zealand's native species.
"Aerial operations are the only way to access this steep and rugged terrain, at present, and an operation like this gives our native taonga the best chance to thrive," he said.
"We work hard to protect our precious native species, so to see rat and possum numbers at an all-time low in the Hunua Ranges is absolutely terrific."