Sangakkara made it a hat-trick in the People's Choice category, receiving the top award from ICC president Alan Isaac.
The 34-year-old batsman and former captain has made almost 1,500 runs at an average above 60 in his last 14 Tests. He has been similarly prolific in one-day internationals, and still keeps wicket in that format too.
Sangakkara emerged the winner of the overall award, from a short-list containing South Africa batsman Hashim Amla - his country's first triple-centurion, against England at The Oval two months ago - Australia captain Michael Clarke and South Africa seamer Vernon Philander.
Twenty-year-old spinner Dockrell was the winner of the 2012 Associate and Affiliate Cricketer of the Year award. The Somerset slow left-armer has taken 52 wickets for his country, across all formats, at an average of just 15.83 since August 2011.
Enid Bakewell was inducted into the ICC's Hall of Fame on Friday. The doyenne of England women's cricket is still playing at the age of 71 - the all-rounder opens the bowling for her club second team with her slow left-arm spin.
England wicketkeeper-batsman Sarah Taylor was named as the women's Twenty20 Cricketer of the Year.
Other winners included: Sunil Narine (West Indies, Emerging Cricketer of the Year), Daniel Vettori (New Zealand, Spirit of Cricket), Richard Levi (South Africa, Twenty20 International Performance of the Year), Kumar Dharmasena (Sri Lanka, Umpire of the Year), Virat Kohli ( India, ODI Player of the Year) and Stafanie Taylor (West Indies, Women's ODI Cricketer of the Year).