Orr served as deputy governor of the RBNZ for four years before joining the New Zealand Super Fund in 2007.
Dominick Stephens, chief economist at Westpac, said markets welcomed Orr's appointment, adding that he was unlikely to veer away dramatically from the inflation target.
"He's an extremely accomplished economist, he's got lots of experience at the Reserve Bank and he's unlikely I think to allow inflation out of the box."
Orr takes up the role at a sensitive time for the RBNZ, as the new Labour-led government plans to add maximising employment to the bank's objectives alongside its inflation target.
"The Board agreed unanimously that he can bring to the role of Governor of the Reserve Bank strong leadership and commitment to ensure the Bank is fit for its wide role in the New Zealand economy," said RBNZ board chairman Neil Quigley in the statement.
Robertson said in the statement that the laws to change the bank's mandate would likely not be in force by March, but the policy target agreement between him and Orr would be "developed in a manner consistent with the direction of reform."
In November, Robertson told Reuters that willingness to focus on lifting employment, alongside inflation, would be key in accepting the RBNZ's choice for the next governor.
Previous governor Graeme Wheeler stepped down in September at the end of his five year term and deputy governor Grant Spencer took on the role for a six-month term while the search for a new chief was under way.