Among those arriving at the Melbourne synagogue are Prime Minister Julia Gillard, Governor General Quentin Bryce, Opposition Leader Tony Abbott and former prime ministers Bob Hawke, Malcolm Fraser and John Howard.
Described by Ms Gillard as "a great Australian" and lauded by many as a man whose leadership and guidance was valued across the country, Sir Zelman died on Thursday, aged 92.
He was appointed as governor-general in 1977, following Sir John Kerr's resignation from what was then a troubled post, given Sir John had used the powers of the office to sack former prime minister Gough Whitlam, dividing the nation.
Sir Zelman served a distinguished and popular four-and-a-half years as governor-general, from December 1977 to July 1982.
The man who appointed him, Mr Fraser, credits him with having restored Australia's faith in the office of governor-general following the controversial tenure of Sir John Kerr.
Having suffered Parkinson's disease for the last 15 years of his life, Sir Zelman died in his Toorak home on Friday, with his wife Lady Anna Cowen by his side.
Sir Zelman was Jewish and his funeral is being held at the Temple Beth Israel synagogue in St Kilda.
His coffin, draped in an Australian flag, is at the front of the synagogue.
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