The appointment comes at a time when New Zealand's Labour-led government, which took the helm in October, is conducting a review of the central bank's mandate in a bid to make good on an election promise to include maximising employment as a monetary policy goal.
Eichbaum had served on the RBNZ's board in between 2008 and 2013 and is currently an academic at Victoria University's school of government.
"Dr Eichbaum brings his experience as a previous Board member at a critical time of change," Finance Minister Grant Robertson said in an emailed statement.
"His understanding of public policy and the place of monetary policy in that context will also be very helpful as the review of the Reserve Bank Act progresses."
Eichbaum has been appointed for a five-year term and is filling a vacancy left by previous board member Rod Carr, who retired in 2017.