Chopra, 80, passed away at a Mumbai hospital this evening.
In his message, the Prime Minister credited the film-maker for establishing the popularity of Indian cinema internationally.
Singh described Chopra as an "icon of Indian cinema" who entertained many generations with his rare creativity.
"He had an aesthetic talent to make his films look larger than life. His flourish to essay romance and social drama was unmatched. He established the popularity of Indian cinema internationally and was honoured by many governments.
"He will be remembered by millions of his fans around the world and his work as a director and producer will be treasured by the nation for many more generations," Singh said.
The Prime Minister sent his condolences to the bereaved family.
Information and Broadcasting Minister Ambika Soni also expressed her condolences.
"Today Indian cinema has lost one of its iconic personalities and a creative genius. Through films, Yashji connected generations together. His idea of portraying love as the essence of life and relationships will fondly be remembered by all movie lovers. His death is a void which will be difficult to fill," Soni said.