"We, Heath's family can confirm the very tragic, untimely and accidental passing of our dearly loved son, brother and doting father of Matilda," his father said.
"He was found peacefully asleep in his New York apartment by his housekeeper. He was down to earth, generous, kind-hearted, life-loving, unselfish, individual (and) extremely inspirational to many."
"We would like to thank our friends and everyone around the world for their well wishes and kind thoughts at this time," Mr Ledger said.
"Heath has touched so many people on so many different levels during his short life but few had the pleasure of truly knowing him."
Celebrity news website TMZ.com has reported Ledger was sick with pneumonia when he died.
"This is the first I'm hearing that," Lieutenant John Grimpal, from the New York Police Department, told Macquarie Radio.
"The medical examiner, once he or she conducts an autopsy, will determine exactly the cause of death."