The 25-year-old Williamson, who captained the Kiwis at the recent World T20, will skipper his national side in all three formats of the game.
New Zealand Cricket CEO, David White, said: “Kane has been a leader within the team for a long time now and already shown himself to be an extremely capable captain.
“He’s respected by his peers and the wider cricket community for his professional approach both on and off the field, and has a superb cricket brain.
“His drive to see the team succeed and his passion for the game are what you look for in a leader. He’s ready for the role and will only continue to grow.”
Williamson, who is currently in India, said: “It’s certainly an honour. I’ve really enjoyed my time spent as captain and believe this team can achieve a lot.
“I’m lucky to have a number of experienced players around me for support and will certainly look to utilise this. We’re all striving for the same thing and that’s to represent New Zealand with pride and win cricket games.
“I’ve certainly learnt a lot from Brendon, as has everyone who has played with him. The culture that he and Mike [Hesson, the coach] have cultivated has been a huge part of this team’s success in recent times.
“We not only have good players, but good people too and that certainly makes any captain’s job easier.”
New Zealand’s next assignment will be a two-Test series in South Africa in August.