Thousands of people took part in processions, which shut down city centre roads and prompted counter-protests.
Shortly after the procession began, police were called to Tradeston Street after reports of a 68-year-old man falling ill.
Emergency services attended, but he was pronounced dead shortly after.
Officers said the death was not being treated as suspicious and a report has been submitted to the Procurator Fiscal.
Grand Orange Lodge Scotland has since posted a tribute on its Facebook page reading: “Jim McHarg Grand Master expresses the condolences of the Grand Orange Lodge of Scotland to the family and friends of Brother John Graham District Secretary Port Glasgow District LOL 19 who sadly passed away yesterday during the Glasgow procession.”
Up to 800 police officers were deployed to manage the event, which saw marches go through the city centre and past Catholic churches.
Police said they made several arrests after “racist and sectarian singing” took place during Orange walks, which shut streets across Glasgow and led to condemnation of anti-Catholic bigotry.
Grand Orange Lodge Scotland said on social media that no marchers were arrested at the event.
Glasgow City Council said 32 roads in the city had been closed off for the processions until the mid-afternoon.
Chief Superintendent Mark Sutherland, Divisional Commander for Greater Glasgow, said on Saturday arrests had been made and condemned the alleged racist and sectarian behaviour “by some of those attending to support” the marches.