The Government's paid parental leave policy increased from 18 weeks to 22 weeks in July and will increase again to 26 weeks in 2020.
For employees paid parental payments currently equal their normal pay up to a maximum of $564.38 a week before tax while partners are only eligible for up to two weeks unpaid leave under the law.
Gail Costa, Cigna New Zealand chief executive, said it made the changes because it wanted to attract the OnePath staff.
"We looked at all their terms and conditions and lined them up with ours."
Under ANZ's ownership OnePath workers already had 26 weeks paid parental leave and KiwiSaver contributions paid over the full year of parental leave as well as unlimited sick leave.
But Costa said they would benefit from Cigna's long service leave.
The company gives a one off week every five years and those who stay at the company for more than seven years get five weeks annual leave.
Cigna staff were previously on 12 weeks full pay for parental leave.
Costa said she hoped the changes would take the pressure off new parents and allow them to stay off work longer.
"We are committed to supporting our people through the early days of parenthood and upon their return to work.
The move comes as unemployment levels in New Zealand hit 3.9 per cent - the lowest level since 2008 when the global financial crisis began to bite.
Costa said it recognised that staff were its most important asset.
"Cigna believes that happy and healthy staff lead to a better service for our customers."
All but six staff from the ANZ business will come over to Cigna, she said.
ANZ New Zealand agreed to sell its life insurance business to Cigna in May for $700 million and received regulatory approval last week for the deal to go ahead.
It has also entered into a 20-year deal to use the bank's network to sell life insurance.
The Cigna/One Path deal continues a shake up in the industry which earlier this year saw AIA buy Sovereign - NZ's largest life insurer - from ASB parent Commonwealth Bank of Australia.
AIA paid A$3.8 billion to buy both CBA's Australian life insurance business CommInsure Life and Sovereign.
AIA also continues to have a long-term distribution deal with ASB to sell its insurance.
Meanwhile AMP has agreed to sell its New Zealand and Australian life insurance business for A$3.3 billion to Resolution Life in the deal which it expects to go through by the second half of 2019, provided it gets regulatory approvals.