Chopra, 80, died on Sunday. His funeral is scheduled to take place on Monday afternoon.
His body is being kept for public viewing in a studio at the production house he set up in the 1970s.
Over five decades, Chopra, dubbed the King of Romance, gave Bollywood some of its biggest blockbusters.
His film studios, Yash Raj Films, helped establish some of Indian cinema's biggest names, including Amitabh Bachchan and Shah Rukh Khan.
Almost all the big names from the industry turned up at the Yash Raj studios on Monday but more importantly, hundreds of fans - people who have watched and loved his movies over decades - have also been allowed to pay their last respects, the BBC's Shilpa Kannan reports from outside the studio.
One of his contemporaries, director Shyam Bengal, said Chopra's death was a huge loss to the industry.
"Yash Chopra revived the big studio format, he brought in a culture that didn't exist before. New talent was encouraged and nurtured under him. It has created a stable of talented directors who have made some of the biggest hits in recent times."
Top Bollywood stars took to the micro-blogging site Twitter to pay tributes to Chopra.
"Yash Chopra - 44 years of association... of creativity, friendship, fun and family ties," tweeted superstar Amitabh Bachchan, who starred in some of Chopra's biggest hits including Deewar (Wall) and Kabhi Kabhie (Sometimes).
In his tribute, Prime Minister Manmohan Singh described Chopra as an "icon of Indian cinema" and said that he had entertained many generations "with his rare creativity".
"His flourish to essay romance and social drama was unmatched," the prime minister said, adding that the filmmaker had established the international reputation of Indian cinema.
Singer Lata Mangeshkar said: "He made me sing in all his films. He was a jovial person... Even when he was angry, he simply kept quiet."
Chopra started his film career working for his brother before establishing Yash Raj Films and going on to produce more than 40 movies - 12 of them as director.
He was behind major hits including Dil to pagal hai (Heart is mad) and Chandni (Moonlight).
Dilwale dulhaniya le jayenge (The big hearted will take the bride), which Chopra produced and his son Aditya directed, is the longest-running movie in India and is still packing in the crowds in Mumbai cinema halls after more than 18 years.
On his birthday last month, he said Jab tak hai jaan (Till I am alive) - being released next month - would be his last film as a director.
Bollywood stars and fans have been paying tribute to one of India's most influential film-makers, Yash Chopra, who died from dengue fever in Mumbai.