He was 74 and is survived by his wife, two sons and a daughter.
Swamy, who competed in the flyweight and bantamweight divisions, was an eight-time national champion, six of them back to back starting 1961.
He never competed in the Olympics for India but went on to be conferred the Arjuna award in 1968.
Swamy also served as a coach with the Sports Authority of Andhra Pradesh.
"It is a huge loss for Indian boxing. Mr Swamy was king of the ring in his prime. He will be missed," former World Cup bronze-medallist V Devarajan said expressing his condolences.
"Its very sad to hear about the loss of Denis Swamy #Olympian and #Arjuna awardee, I express my sincere sympathy his family. RIP," she wrote in her twitter handle.