Mr McGrady, 78, a founding member of the party, died in hospital on Monday after a long illness.
His nephew, Father Fergal McGrady, who was the main celebrant at the funeral at St Patrick's Church in Downpatrick, described his uncle as a "unifier by nature".
"A Christian, a democrat and a patriotic Irishman, he was, in the eyes of fair-minded observers, critics and supporters alike, a gentleman of honour," Fr McGrady said.
The Downpatrick-born politician and father-of-three was the Member of Parliament for South Down for 23 years, until his retirement in 2010.
Current party leader Dr Alasdair McDonnell, former leader John Hume, former SDLP Stormont deputy first minister Seamus Mallon and the party's current South Down MP Margaret Ritchie were among hundreds of people who joined members of the McGrady family at the funeral service.
A one-time chairman of the SDLP and a vocal supporter of the peace process, Mr McGrady was well respected by all political sides in Northern Ireland.
Northern Ireland Secretary Theresa Villiers, Sinn Fein Deputy First Minister Martin McGuinness, Democratic Unionist Economy Minister Arlene Foster, Ulster Unionist leader Mike Nesbitt and Alliance Party leader and Justice Minister David Ford all attended this morning's funeral.
Mr McGrady's wife, Patricia, died in 2003. He is survived by his daughter, Paula, and two sons, Jerome and Conaill.
Fr McGrady went on: "He was in the main more interested in bettering the lot of people socially and materially than in any aspect of political belief.
"Newsreels as far back as 1969 show him trudging through the snow, sometimes with Patsy, canvassing, helping people on ordinary-day issues, his manner generally quiet and reassuring - 'Steady Eddie'.
"He was a unifier by nature; words carefully chosen, measured, conciliatory; a moderating influence. He espoused Christian and family values."
The cleric said his uncle was not afraid to take on big business interests and also cited his campaign against the nuclear waste disposal plant at Sellafield in Cumbria and its alleged health impact on Ireland.
Bishop of Down and Connor Noel Treanor also reflected on Mr McGrady's life.
"It was with great sadness that I learned of the death of Mr Eddie McGrady after heroically facing a long period of illness," he said.
"I pay tribute to the immense contribution of Eddie McGrady to the political arena, firstly as a founding member of the SDLP espousing the highest ideals and virtues of constitutional democracy, and also in his tireless capacity to reach out across his South Down constituency to all those in need.
"Motivated by faith, strengthened by the values of integrity, courage and justice and astutely attentive to social and community concerns, he was a popular politician who engaged effectively with those he met in his public office."
After the funeral service, Mr McGrady's coffin was taken to nearby Saul parish church for burial.
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