Kohli beat Hashim Amla, Kumar Sangakkara and Michael Clarke to bag the award. Kohli was the top run-getter for India in both Tests and ODIs last year, and his career-best 183 came against Pakistan in the Asia Cup in March last year.
Former Pakistan captain Zaheer Abbas was honoured with the lifetime award.
In the special India-Pakistan award category, retired batting great Inzamam-ul-Haq, also a former captain, got the award for the best ODI bastman, India's little master Sunil Gavaskar the best Test batsman, Kapil Dev the best Test bowler and Wasim Akram the best ODI bowler.
Pakistan's former explosive opener Saeed Anwar got the best audience choice awards for the 2011-12 season.
Delhi youngster Unmukt Chand, who led India to the U-19 World Cup win last year, got the inaugural Indian Youngster of the Year award.
"It is a great honour for me. The World Cup win was special for us. This is my second award and I hope such awards will boost my confidence in the future," he said.
Legendary fast bowler Akram, who also collected the award on behalf of the Pakistan team, said it was a great honour for him.
"It was in 1999 when I got the award for the Pakistan team. It was a great honour for me. Now as I collect the award on behalf of the team, I feel honoured again," said the former Pakistan captain.
Kapil Dev also lauded the Pakistan team for its impressive performance in India. Pakistan have already sealed the three-match ODI series 2-0. The last and the final ODI to be held here Sunday is now a dead rubber.
"The Pakistan team has been exceptional. They deserve to win. They have a great batting and bowling attack," said Kapil.
Asked what went wrong for India in the series, Kapil said: "The less we say it's better. Let us enjoy the chilly Delhi weather. Day after (Sunday) we will enjoy some better cricket. Indian cricket team has a good reputation but they haven't played well this time. Hopefully they will do well in the coming days."
On getting the award, Kapil said: "It is tough to say how difficult it is when you play against Pakistan. The pressure takes over you. You have to hold your nerves."
The awards ceremony was attended by former cricketers from both sides of the border like Gavaskar, Kapil, Yashpal Sharma, Ajay Jadeja, Akram, Izamam, Abbas, Anwar and Rameez Raja.