Director Terry Gilliam was a close friend of Ledger's and plans to keep in footage already filmed of the actor
Production was suspended immediately after the 28-year-old was found dead in his rented New York apartment.
Shortly after Ledger's death, the film's producers paid tribute to the Australian actor, calling him "a great actor, a great friend and a great spirit".
Ledger was farewelled at a memorial service in Perth a week ago. His former fianc, actress Michelle Williams, attended, but their two-year-old daughter Matilda was absent.
Williams and Ledger met on the set of Brokeback Mountain, and broke up a four months prior to his death.
The actor had subsequently suffered from insomnia and had been taking sleeping pills and anti-anxiety medication.
Earlier this month New York's chief medical officer, Charles Hirsch, ruled Ledger died from the combined effects of six prescription drugs.