Ledger was midway through making the movie when he died from an accidental drug overdose in January 2008.
Director Terry Gilliam chose to fill his character in the remaining scenes with an ensemble cast of Jude Law, Colin Farrell and Depp, who starred in his 1998 movie Fear and Loathing in Las Vegas.
Depp admits it was tough filling the Oscar winner's shoes, but he felt honoured to share the screen with an actor he admired.
He tells Moviefone.com, "Though the circumstances of my involvement are extremely heartrending and unbelievably sad, I feel privileged to have been asked aboard to stand in on behalf of dear Heath...
"He was the only player out there breathing heavy down the back of every established actor's neck with a thundering and ungovernable talent that came up on you quick, hissing rather mischievously with that cheeky grin, 'Hey... get on out of my way boys, I'm coming through!' And does he ever!"