Bollard will step down after his second five-year term expires on September 25.
Wheeler's extensive experience has made him a highly respected figure in world financial markets and within New Zealand, English said.
"We were fortunate to have someone of his calibre available for this important role."
The Reserve Bank board of directors recommended Wheeler's appointment to English after an extensive recruitment process domestically and internationally.
"Given his experience and standing, combined with his technical and leadership qualities, the board considered that he has all the qualities required to become governor and chief executive of the Reserve Bank," English said.
Wheeler was employed by the World Bank from 1997 to 2010, his most recent roles included managing director operations from 2006-2010, and vice-president and treasurer from 2001 to 2006.
He was previously at the New Zealand Treasury as deputy secretary and treasurer of the Debt Management Office.
Wheeler is a New Zealander but currently lives in the United States where he runs his own advisory business.
Wheeler will be governor-designate until a new policy targets agreement is finalised in the next few months. This is required before a new governor is appointed.
