All Commonwealth countries, including New Zealand, will need to change their laws to ensure Prince William's firstborn is third in line for the throne.
Under the current laws, if the first-born of Prince William and the Duchess of Cambridge were a girl and then they had a boy, the male would take precedence in line for the throne.
The Queen reigns as she had no brothers and her father died.
In October last year, British Prime Minister David Cameron announced changes to the succession laws that could mean Catherine and William's first child would become third in succession, regardless of whether it is a boy or girl.
However, for those changes to be enacted, all commonwealth countries, which have the Queen as their monarch, have to change their legislation so that males would no longer have precedence as heir.
The agreement also means an end to a ban on a future monarch marrying a Catholic, a stipulation dating back 300 years.
A spokeswoman for New Zealand Prime Minister John Key said the Cabinet had approved changes to New Zealand's legislation, and the Justice Ministry was developing a Royal Succession Bill.
"However, we are waiting for the UK to introduce its bill. We understand that this is expected to be soon and so we would expect New Zealand's legislation to be introduced to the House in the first part of 2013," the spokeswoman said
All Commonwealth countries will need to do the same in order for the British bill to be valid.
- The Press
Have you adjusted to the new alcohol limits for drivers?Related story: New alcohol limits catch first drivers