Conway will embrace a casual agreement to be available for international assignments, which means that he will be available to play for the national team when the schedule does not overlap with his franchise commitments.
"Firstly, I'd like to thank New Zealand Cricket for their support through this process," Conway said in a video posted by Blackcaps on 'X'.
"Playing for the Black Caps is still the pinnacle for me and I'm hugely passionate about representing New Zealand and winning games of international cricket."
Conway maintained that this decision was taken prioritising the best interests of his family.
"The decision to move away from a central playing contract isn't one I've taken lightly, but I believe it is the best for me and my family at this present time," he added.
Williamson recently opted to skip the white ball series against Sri Lanka to play in the SA20, whereas speedsters such as Adam Milne and Lockie Ferguson have also forged similar agreements with the NZC.
"We're delighted with Devon's decision to commit to the Blackcaps - he's a quality player who's made a strong contribution to the team over the past few years," said NZC chief executive Scott Weenink.
"In the current environment it's important to have flexibility in our system to navigate some of the challenges posed by franchise cricket - and this is another example of how we're working hard to retain our best players," he said.
While Conway is a central figure for Chennai Super Kings, the 25-year-old Allen is not a regular in the IPL circuit.
But he has other avenues such as stints with the likes of San Francisco Unicorns in Major League Cricket (MLC), and for both Southern Brave and Birmingham Phoenix in 'The Hundred' in England.