Kapur, 70, directed Ledger in his 2002 movie "The Four Feathers". Ledger died on January 22, 2008, New York City, from an accidental intoxication from prescription drugs.
"He went too young. But then I always told Heath there was an ancient wise spirit in his young mind. His spirit rose," Kapur wrote on Twitter.
The "Mr India" director has also wrapped the shoot of the pilot of his TV drama "Will", which tells the wild story of young William Shakespeare's arrival onto the theatre scene in 16th century London.