"As a close knit and very private family we have observed you so determined yet quietly travelling in your self-styled path in life, nothing would get in your way ... no mountain too tall, no river too wide," the family said in a death notice published Friday in The West Australian.
"You dreamed your dreams and lived them with passion and intelligent commitment. We have been privileged to accompany you on a ride through life that has simply been amazing and through it all we have loved each other beyond imagination," the notice added. "Our hearts are broken."
In a separate notice, Ledger's father Kim wrote: "Heatho, Beef ... my beautiful boy, so loving, so talented, so independent ... so no more chess games mate ... this is it, couldn't beat you anyway.
"We were one, in soul and commitment, just ... father and son."
The actor's sister, Kate, said she could "hardly breathe" as she tried to write her tribute.
"We were the ultimate soul mates," she said.
"You were so many things to so many people, but to me you were just my little brother. You will never leave my thoughts, 'Roast', ever."
Ledger's mother, Sally Ledger-Bell, said the family would always be there for his 2-year-old daughter, Matilda, whose mother, actress Michelle Williams, was separated from the actor.
Mary-Kate Olsen called Ledger a "friend" in a brief statement released Friday, the first word from the "Full House" star since the Australian-born actor's death.
Released by her publicist, the statement, in its entirety, reads: "Heath was a friend. His death is a tragic loss. My thoughts are with his family during this very difficult time."
The 28-year-old actor was found dead in his New York apartment Tuesday, where police also found several bottles of prescription drugs. Authorities suspect a possible overdose, but toxicology tests have not yet determined the exact cause of death.
His body was taken to the Frank E. Campbell funeral home in New York for a private viewing. Then his casket was carried out of the buidling, to be sent back to Australia for burial. A funeral service will also be held in Los Angeles.
Australian model Sophie Ward, whose sister reportedly had a brief romantic relationship with Ledger last year, said she was planning to fly to the United States for his funeral.
"I think we're going to L.A.," Ward told the newspaper. "This is just a funeral service. He'll probably be buried in Perth."
Ward, 22, is the older sister of Australian-born supermodel Gemma Ward.
"My sister will probably make a comment at the funeral," Ward was quoted as saying. "Heath was an amazing actor and person and she is very upset. She has lost a very good friend."
Sophie Ward also told the newspaper that Ledger had been "a bit edgy" over his recent split with Williams.
"He was clean and wasn't drinking any alcohol or taking drugs," Ward said. "He smoked cigarettes, but that's about it. He was drinking diet Coke when we were together and he said he was very committed to not drinking alcohol. I don't believe he took his own life deliberately."
