Goswami, 80, was unwell for the last few days and he was admitted at a private hospital.
He was suffering from heart-related issues and his health had deteriorated since Monday.
Prime Minister Narendra Modi expressed condolence on the death of Goswami.
He wrote on Twitter: "Saddened by the passing away of Shri Nipon Goswami who made a pioneering contribution to the Assamese film industry. His diverse works will be remembered by several film lovers. Condolences to his family and admirers."
Assam Chief Minister Himanta Biswa Sarma also condoled the veteran actor's death.
Other eminent personalities of the state have expressed grief over Goswami's demise.
Goswami was born in Assam's Tezpur town.
He was an alumnus of the prestigious Film and Television Institute of India.
He debuted in the Assamese cinema as a child artist in 1957.
The octogenarian worked in a number of Assamese films and was a very popular face.
Besides the silver screen, Goswami was also active in mobile theatres, advertisement commercials, and TV soaps.
His father Chandradhar Goswami was also a famous actor and his mother Nirupama Goswami a singer.
The Assam government has announced that his last rites would be performed with full state honour.