Mr Wheeler and Finance Minister Bill English signed a new policy targets agreement (PTA) which sets out specific targets for maintaining price stability.
The new agreement takes effect on September 26 and continues to require the central bank to keep consumer price inflation between 1% and 2%, with a focus on keeping future average inflation near 2%.
A stronger focus on financial stability, by including asset prices in the range of indicators the bank monitored, was part of the new PTA.
The central bank was required to consider the soundness and efficiency of the financial system in setting monetary policy, Mr English said.
"I believe the existing policy targets agreement has serviced New Zealand well and there are benefits in maintaining consistency in the agreement. Therefore, I did not feel that any major changes were required," he said.
Outgoing governor Alan Bollard recognised asset price stability as a key topic of debate in a speech he gave back in 2004.
"The sharp end of this is whether monetary policy should seek to prevent or at least reduce asset price bubbles. This is exemplified by questions such as whether Japan's long-running recession and the US 'tech wreck' could have been ameliorated by monetary policy constraining the events that preceded them."
By an asset price, Dr Bollard meant the price of something that was bought to generate income or to sell for a profit later.
Examples were physical assets - like housing, land, other buildings and collectables like paintings or exotic cars - and financial assets such as shares, bonds and other financial instruments.
Consumer prices included things bought to consume, like milk, petrol, a visit to the doctor and ordinary cars.
"Remember also that asset prices often behave more erratically than consumer prices, being slower to react to changes in supply and demand. Prices of, for example, fruit and vegetables move constantly to match up buyers and sellers. Asset prices are seldom that appealing in terms of classic economics," Dr Bollard said.
Mr English wanted to ensure the PTA kept reflecting best international practice.
The Government was also continuing to work with the Reserve Bank and the Treasury to assess whether further macro-prudential tools could help moderate credit cycles by building additional resilience when it was likely to be needed, Mr English said.
Labour finance spokesman MP David Parker said new targets for the incoming Mr Wheeler could not properly address the biggest issue facing the export economy, the high dollar.
"The high dollar is costing Kiwis jobs. National must accept that unless changes are made to the Reserve Bank Act, the primacy which by law must be given to inflation will mean inadequate attention is paid to the exchange rate. Our dollar will remain overvalued. That means more businesses will suffer and more Kiwis will lose their jobs."
The Government should admit the policy of placing inflation over the exchange rate had passed its use-by date and change the law, Mr Parker said.
"Giving primacy to inflation is last century's fight. It's time to move on," he said.
At a glance
• New policy targets agreement from September 26
• Inflation to be between 1% and 3%
• Average inflation to be 2%
• Asset prices to be considered
