Mr Peachey informed Mr Goodfellow of his decision yesterday, following a meeting with party executives and electorate staff on Sunday at which his health was discussed.
Nominations will open tomorrow and close on October 14. A final selection is expected around October 25.
"This has been an understandably difficult decision for Allan who has remained committed to serving Tamaki as its Member of Parliament. We wish him well and plan to do him proud by running a strong campaign in this important electorate,'' said Mr Goodfellow.
Mr Peachey, 61, a former principal of Rangitoto College, holds the blue ribbon Tamaki seat with an enormous 17,020 vote majority.
The National Party candidacy for Tamaki, for many years held by former National Party Prime Minister Rob Muldoon and then by Clem Simich, is likely to be keenly contested.