The Sri Lankan veteran was also named the ICC Test Cricketer of the Year, besides winning the People's Choice Award.
During the period under consideration, the 23-year-old Kohli, played 31 ODIs and compiled 1,733 runs at an outstanding average of 66.65, including eight centuries and six half-centuries.
His highest score of 183 came against Pakistan in the Asia Cup on March 18.
The 32-member expert panel preferred Kohli, who beat off competition from his skipper Mahendra Singh Dhoni, Sangakkara and Sri Lanka's pace spearhead Lasith Malinga.
"I think I have tried to keep things as simple as possible and it's worked for me on the field. This year has been a learning curve along the way from the seniors in the team. It's been an all-round effort and I'm very happy to have won this award," Kohli said upon receiving the award.
"It's always nice to be recognised by the ICC and it's a great feeling and it's the first time I've won one of these awards and it feels great," the Delhi lad added.
In the 50-over format, Kohli has so far scored 3886 runs from 90 matches at an average of 51.81. In Tests, he has scored 703 runs from 10 matches at an average of 41.35. He has two centuries and five fifties, with 116 being his best.
In 14 Tests, Sangakkara scored 1,444 runs at an average of 60.16, including five centuries and five half-centuries. In addition, he played 37 ODIs, hitting 1,457 runs at 42.85, with three centuries and nine half-centuries. He has also effected 42 dismissals in the ODIs.
"This is an amazing honour and I've seen the people who have won it before me and the nominees too, to be named alongside them is wonderful," Sangakkara said.