The one-day batting award went to Kohli for his unbeaten knock in India's successful chase of 320 in under 37 overs last year. The 86-ball blitzkrieg kept India alive in the tournament.
The Test batting award went to Kevin Pietersen, for his 186 against India last December.
Vernon Philander took the Test bowling award for his five-for against England at Lord's, while the ODI bowling award was clinched by Thisara Perera for his six for 44 against Pakistan in Pallekele, which paved the way for Sri Lanka's 76-run win.
The T20 winners were Marlon Samuels for his 78 in the World Twenty20 final against Sri Lanka, a match where 13 batsmen made single-digit scores; and Lasith Malinga's five for 31 against England earlier in the tournament.
Saeed Ajmal bagged the readers' choice category.
In the six-year history of the awards, Virender Sehwag, Lasith Malinga, Umar Gul and Dale Steyn have each won two awards. Sachin Tendulkar tops the table with three wins.