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He stood down from his role earlier this year because of ill health but was to officially remain in post until February 2017.
Mr Murphy played football and hurling for clubs in Down and was a county selector in the early 1990s.
A lengthy career in administration included being a former member of the GAA Central Council and vice-president of the GAA.
Mr Murphy served as vice-president and president of the Ulster Council before being appointed provincial secretary, a position he held for 16 years.
"Danny was an outstanding leader who provided unstinting dedication to the GAA in Ulster for over 35 years," said Ulster GAA President Michael Hasson.
"It was very fitting that Danny's leadership was honoured earlier this year by the First Minister, Arlene Foster, and Deputy First Minister, Martin McGuinness, at Stormont in recognition of his efforts in promoting reconciliation, tolerance and respect across all communities.''
Mr Murphy's funeral mass will take place on Saturday, 10 December in St Mary's Church, Burren.
Ulster Council secretary Danny Murphy has died at the age of 67.