Williamson made 948 ODI runs at an average of 59.25 in 2019.
Ross Taylor and women's skipper Sophie Devine bagged the honour in the T20Is.
All awards were presented online because of the COVID-19 pandemic.
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Williamson was outstanding throughout last year, scoring 948 runs at an average of 59.25 to finish as Black Caps' highest run-maker for the year in ODIs. His exploits including an excellent 2019 World Cup in UK, where Williamson made 578 runs, including two hundreds, to bag the "Player-of-the-Tournament" award.
"Kane was simply exceptional at the ICC Cricket World Cup last year," New Zealand head coach, Gary Stead, said in a media release.
"Kane fully deserved his selection. He builds great partnerships with our well-established middle order and when he bats deep in an ODI innings, we'll invariably be in a good position to win most of those matches."
"He leads the team well, he has his own style and certainly the respect of his peers. His calm, purposeful demeanour flows through his leadership and, in turn, the team."
Black Caps batsman Taylor made 330 runs in T20Is last year at a strike-rate of 130.
"A man of Ross' international experience is very valuable in the fast and furious nature of T20 cricket," Stead said for the 36-year-old.
"He has the ability to sum up batting conditions quickly and accurately in a variety of venues and countries. This is a skill which serves the team well and helps us adapt plans quickly in the shortest form of the game."
Devine was among the best female T20I cricketers of the year 2019, with 429 runs at an average of 71 and strike-rate of 132 before being honoured by NZC.
Bates was superb during White Ferns' only ODI series last year against South Africa, as she made two half-centuries in three games and finished with 142 runs at an average of 42.