“Playing for New Zealand is something I treasure, and my desire to give back to the team remains undiminished.
“My life outside cricket has changed however – spending more time with my family and enjoying experiences with them at home or abroad is something that’s even more important to me.”
A statement from New Zealand Cricket (NZC) said Williamson might accept a central contract in the future.
NZC chief executive Scott Weenink said: “This is a good way to help keep Kane in the international game so that he continues to play a major role for the Black Caps – both now and in the years to come.
“NZC has a strong preference to select centrally contracted players for the Black Caps, however we’re happy to make an exception for our greatest ever batter – especially as he remains so committed to the team.
“I know it sounds a bit counterintuitive, but I’m very encouraged by this development.”
England will play three Tests in New Zealand in December.
Williamson’s decision to step down as white-ball captain comes after New Zealand were knocked out in the first round of the T20 World Cup.
It is the first time the Black Caps have not reached the semi-finals of a T20 or 50-over World Cup since 2014.