Ledger was previously nominated for an Oscar for his 2005 performance as a gay cowboy in the film Brokeback Mountain, although he did not win the award.
The actor's Oscar will eventually go to his three-year-old daughter, Matilda Ledger, by his former fiancee, actress Michelle Williams.
The Academy of Motion Picture Arts and Sciences decided Matilda should receive the Oscar when she reaches 18 years old.
Other award winners included Penelope Cruz, who became the first Spanish-born actress to pick up the best supporting actress award for her performance as artist Maria Elena in Woody Allen's romantic comedy Vicky Cristina Barcelona.
"Thank you Woody for trusting me with this beautiful character. Thank you for having written over all these years some of the greatest characters for women," the 34-year-old Cruz said as she accepted the Oscar.
However, it is Slumdog Millionaire, the widely acclaimed film set in the slums of Mumbai, that is tipped to scoop this year's award for best picture.
Danny Boyle, director of Slumdog Millionaire, picked up the best director award and the film's seventh Oscar of the night.
Slumdog Millionaire also won best adapted screenplay, best cinematography, sound mixing, film editing and original score at the ceremony.
The film, about a poverty-stricken slum-dweller who competes for love and money on the Indian version of the television gameshow Who Wants to be a Millionaire?, also won the Oscar for best original song.