The current MP for Port Hills is Ruth Dyson – who has held the seat (which has undergone several boundary changes) since 1993.
She announced earlier this years she will retire from politics before the 2020 election.
Korako said he expected National to do well in the 2020 race for Port Hills.
"I will be there to support the new candidate when they are selected."
In a statement, Bridges praised Korako and his contribution to politics over the past half-decade.
"Nuk was instrumental as chair of the National Party Māori Caucus in developing Māori capability within the National Party. He established the regional Kahurangi National Māori Groups and will continue this work."
Korako said it has been privilege and a pleasure to work for the Port Hills community.
"We have shared some trying times together. The earthquakes, the Port Hills fires and the recent terror attack. I leave knowing our community has grown together and become stronger."
He said he was especially proud to have chaired the Māori Affairs Select Committee - shepherding 16 Treaty Settlements to a conclusion.
"The Parihaka settlement is a particularly poignant one for me. Te Whiti and the Taranaki men that were wrongfully imprisoned were looked after by my Rāpaki hapū and so our ties run deep."
Korako said his focus will now turn to a range of opportunities that he will pursue.
He is also looking forward to spending more time with his wife Chris and their four sons.