The silver car was presented by Chopra to the Bollywood icon at the latter's Janak office in northwest Mumbai's Juhu suburb.
"Mr Bachchan's performance is simply stunning in 'Eklavya' and I felt such an accomplished performance deserves an extra special acknowledgement and what better than a Rolls Royce for a person who has a passion for cars," Chopra said.
Asked for his reaction, Bachchan said, "I am over the moon. I wanted to work with Vidhu for a long time and this finally happened after a long wait of 30 years."
When Bachchan was asked to compare his turn in "Eklavya" with that in Sanjay Leela Bhansali's "Black", as both directors had touted his performance in their respective films as the best, he said, "I have realised why Sanjay is a perfectionist, because he worked under Vidhuji for eight years."
Commenting on media reports that he had presented his son Abhishek a Bentley on his birthday on February 5, Bachchan said, "I have not gifted the Bentley to him."