Emergency services closed part of the thoroughfare at around 5.40pm to tend to the man who was pronounced dead at the scene.
His death is being treated as unexplained but police said there do not appear to be any suspicious circumstances.
A police spokesman said: “Police in Edinburgh can confirm that a man has died on a bus in the Leith area of the capital this evening.
“Emergency services were called to Leith Walk around 5.40pm after concerns were raised regarding a passenger who was travelling on the top deck of the Number 16 bus.
“Paramedics boarded the bus to treat the man, however he was pronounced dead at the scene.
“Police are currently working to establish the circumstances of the man’s death, which is being treated as unexplained.
“At this stage there is nothing to indicate there are any suspicious circumstances.”
Police are appealing to anyone with any information regarding the incident to contact them.