Yorkshire duo Jonny Bairstow and Joe Root have also made the one-day international team of the year.
India captain Kohli lifted the Sir Garfield Sobers Trophy for the ICC Cricketer of the Year and was also named the Men’s Test and ODI Player of the Year.
The 30-year-old scored 1,322 runs, including five centuries, at an average of 55.08 in 13 Tests and 1,202 at an astonishing 133.55 with six hundreds in one-day internationals.
Kohli said: “It feels amazing. It’s a reward for all the hard work that you do throughout the calendar year.
“I feel really grateful and very, very happy with the team doing well at the same time as performing.
“Having recognition at the global level from the ICC is something you feel proud of as a cricketer because you understand that there are many players playing the game.”
Kohli was named captain of both the Test and ODI teams of the year and although England did not have a representative in the former, Bairstow, Root, Jos Buttler and Ben Stokes all made the latter.
Aaron Finch’s world-record 172-run T20 score against Zimbabwe has won him the Performance of the Year award for the second time.
The 32-year-old Australia opener plundered 16 fours and 10 sixes as he smashed his own record of 156 during his 76-ball onslaught in Harare in July last year to regain the prize he won in 2013-14.
India’s 21-year-old wicketkeeper-batsman Rishabh Pant was named Emerging Player of the Year after launching his Test career with a six and never looking back.
He scored a century and two 50s on his way to a total of 537 runs in eight Tests during the voting period and claimed 40 catches and two stumpings, and also contributed in one-day international and T20 matches.
Other awards: Associate Player of the Year, Scotland batsman Calum MacLeod; Spirit of Cricket award, New Zealand’s Kane Williamson; Umpire of the year, Sri Lankan Kumar Dharmasena; Fans’ Moment of the Year, India winning U19 World Cup in New Zealand.