An internal investigation at Immigration New Zealand was referred to the SFO in August 2013.
"Bribery is bad for New Zealand businesses and citizens and bad for New Zealand Inc.," said SFO director Julie Read.
"This is plain in the case where a bribe is paid to secure a contract - but a bribe paid to circumvent the rules also causes significant harm.
"The rules, whether they are about immigration or anything else, are intended to apply to everyone equally.
"Circumvention of the rules undermines any fairness in society."
Ms Read said she hopes the case will deter "all those who may be tempted to engage in corrupt conduct".
Immigration New Zealand said it took all allegations of misconduct "extremely seriously" and investigated all instances of suspected impropriety thoroughly.
"Misconduct that undermines the integrity of the immigration system and reputation of the organisation will not be tolerated.
"While misconduct of this nature is extremely rare it is nonetheless very disappointing, particularly to the 1400 Immigration staff worldwide who pride themselves on the integrity of which they make half a million visa decisions each year."