He served as Grand Secretary of the Grand Orange Lodge of Ireland for the past 12 years.
He was part of Orange delegations which met senior political and civic figures, including successive First Ministers and Secretary of States, US ambassadors, Taoiseach Edna Kenny, former Irish President Mary McAleese, the then leader of the Catholic Church in Ireland, Cardinal Sean Brady, and the SDLP, among others.
The Order described Mr Nelson as its "heartbeat" and "perhaps its greatest ever advocate" demonstrating the impact the Dromore solicitor made during his time in his pivotal role.
Mr Nelson is survived by his mother Meta, his sister-in-law Janet and nephews Scott and Stuart.
He funeral service will take place on Thursday in St John's Parish Church, Kilwarlin, with interment afterwards in the adjoining churchyard.
Leading the tributes was the First Minister, Arlene Foster, who described him as a "towering figure" in Orangeism.
Grand Master of the Grand Lodge of Ireland Edward Stevenson described Mr Nelson as the heartbeat and perhaps the greatest advocate of the Orange Institution. He added: "Drew was a towering figure within the Orange fraternity, whose commitment and devotion to the principles of Orangeism are simply unrivalled. No other individual, over the course of the past decade, has done more to champion the cause of the Institution and its membership."
He said Mr Nelson's greatest legacy was the visit by Prince Charles to the birthplace of Orangeism, Loughgall, earlier this year.
Deputy Grand Master Harold Henning described Mr Nelson as the "engine room" of the Institution.
"No other Orangeman, of perhaps any generation, will ever match his motivation and drive to see the Institution succeed and flourish... Drew was a trailblazer for Orangeism, the like of which we will never see again," he said.
Arlene Foster added: "I have known Drew for many years. He was a dear friend and I, and many like me, will miss his wise counsel. He was a towering figure in the Orange Order, doing so much to contribute to its ideals and its reputation. His commitment to the principles of the organisation was something that was widely admired."
The Queen’s University law graduate was a solicitor for 35 years, with his own practice in Dromore, Co Down. He was also a former president of Dromore Chamber of Commerce.
Previously, he was District Master of Lower Iveagh District in Co Down. Drew was a member of Listullycurran LOL 616. He was also a member of the Royal Black Institution.
Mr Nelson was a part-time officer in the now disbanded UDR and was a member of the Ulster Unionist Party until taking up the post of Grand Secretary. He previously completed an army commission course at Sandhurst University.
As a UUP councillor from 1993 to 1997 and a former chair of Banbridge District Council, now part of the new Armagh, Banbridge and Craigavon Borough Council. And was chairman of the Orange Community Network up until his death.