 Ledger died from an accidental overdose of prescription drugs |
Filming was suspended when the star was found dead in January.
Jude Law, Johnny Depp and Colin Farrell will now appear as Ledger's character, but scenes he had previously filmed will be included in the movie.
Gilliam said he was hoping "to touch people's hearts and souls as Heath was able to do" through the film.
'Blessing and support'
"I am grateful to Johnny, Colin and Jude for coming on board and to everyone else who has made it possible for us to finish the film," said Gilliam.
"I am delighted that Heath's brilliant performance can be shared with the world."
He added filming on the British-Canadian production had resumed in Vancouver "with the blessing and support of Heath Ledger's family".
It had been suggested that Ledger's role would be completed using CGI (computer generated imagery) special effects, which is what happened when Oliver Reed died during the making of Gladiator.
 Farrell was in Ledger's film with Johnny Depp and Jude Law |
The film's producers said other allowances had been made.
"Since the format of the story allows for the preservation of his entire performance, at no point will Heath's work be modified or altered through the use of digital technology," they said.
"Each of the parts played by Johnny, Colin and Jude is representative of the many aspects of the character that Heath was playing."
Newspapers have reported the story will involve a magical mirror that takes people into different dimensions, allowing Gilliam to switch between actors.
Daughter 'provided for'
Ledger died from an accidental overdose of six different types of prescription drugs in his New York apartment.
At the time, the film's makers described Ledger as "a great actor, a great friend and a great spirit" and said Gilliam and his producers would be "assessing how best to proceed".
It is thought the movie will be released early next year.
Ledger's father, Kim, has also stated that Ledger's daughter, Matilda, and his ex-fiancee actress Michelle Williams would be provided for.
"Matilda is our absolute priority, and Michelle is an integral part of our family," he said. "They will be taken care of and that's how Heath would want it to be."
