Williamson, who returned from paternity leave this month, hit a match-winning century in the opening Test against Pakistan to help New Zealand win by 101 runs at Mount Maunganui on Wednesday.
The New Zealand skipper described it as “humbling” to overtake Smith, who held the top spot for 313 days this year, and Kohli, who was number one for 51 days.
“They are incredible players of our generation,” Williamson said as he arrived in Christchurch ahead of the second Pakistan Test which starts on Sunday.
“Those two players are the best so for me to sneak up perhaps in some way, is very surprising and humbling.”
All three players were this week named in the International Cricket Council's team of the decade with Smith also named as the individual Test player of the decade. Kohli took the award for the best one-day player.
Smith is in the middle of a rare slump in form and dropped behind Kohli after registering four single-digit scores at the halfway stage of the ongoing four-Test series against India.
Kohli, who topscored for India in their eight-wicket thrashing by Australia in the series opener in Adelaide, has returned home for the birth of his first child.
India's stand-in skipper, Ajinkya Rahane, jumped to number six after his stellar hundred in the second Test inspired the tourists to a series-levelling victory in Melbourne.
Australia's Pat Cummins remains the top-ranked Test bowler, while compatriot Mitchell Starc jumped two places to enter the top five.
India spinner Ravichandran Ashwin (seventh) and quick Jasprit Bumrah (ninth) improved their top 10 positions after their impressive performance in the Melbourne Test.
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