The 25-year-old had already skippered the Black Caps on 36 occasions in one-day and Twenty20 encounters.
However, following the recent retirement of Brendon McCullum, Williamson will now also lead the Test team.
"It's certainly an honour. I've really enjoyed my time spent as captain and believe this team can achieve a lot," he said.
"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."
Williamson has made 48 Test appearances, as well as amassing a further 93 ODI games and 35 T20I outings.