The New Zealand dollar was largely unmoved by the announcement - holding firm above US73c.
That suggests markets are comfortable with the process around the departure and the interim appointment.
There has been speculation for some time about Wheeler's intentions, given he is now 65 and would have been bumping up against Reserve Bank age limits by the end of a second term.
In a statement Wheeler indicated he had always intended to serve just one term.
"It has been a great privilege to serve in this role, and in the remaining eight months I will remain fully focused on the economic challenges and opportunities facing the New Zealand economy. It was my intention, when I was appointed, to serve one term, and then to take on governance roles."
In his preview of this Thursday's Monetary Policy Statement, Westpac chief economist Michael Gordon highlighted uncertainty over the Governor's future as one of the most notable risks around monetary policy this year. The other risk being the general election.
"If Wheeler steps down, the RBNZ Board is likely to make an appointment around June or July. And regardless of whether there's a change of Governor, a new Policy Targets Agreement will have to be negotiated with the Finance Minister before the next term begins," Gordon writes.
"To complicate things, the election will be held on 23 September, just days before the Governor's term begins. If the election results in a change of government, it's possible that the PTA could be renegotiated a second time this year."
With a change of Government comes the possibility that the Reserve Bank might be reviewed and targets modified.
The appointment of Spencer will be seen as a sensible interim move while a broader national and international search is carried out for a new Governor.
Spencer is Deputy Governor and Head of Financial Stability, a position he has held since 2007. He serves as chair of the OECD's Committee on Financial Markets, and has held senior management positions at the Bank in economics and financial markets.
In 1995-2004, he was with the Australia and New Zealand Banking Group, holding senior management roles in treasury and strategy in New Zealand and Australia. He has also served terms with the International Monetary Fund as a Special Advisor, European Department, and as New Zealand's Alternate Executive Director.