The patriarch of the Coptic Orthodox Church led Egypt's minority Christians for the last four decades, a period when government policies often restricted the activities of Christians.
His death comes at a time when uncertainty remains over their future in the new Egypt following a series of deadly attacks on the community since the uprising that toppled Hosni Mubarak.
Large crowds have lined up outside St Mark Cathedral in Cairo to view the pope's body.
Rev Fr Simon said: "His Holiness served for over 40 years as the Pope of the church; in this time with the grace of God he has impacted profoundly on the lives of those who are within and outside of the church. He will be remembered as the charismatic spiritual leader of this era, "Athanasius of the 21st Century".
The Rev Hon Fred Nile MLC, Leader of the Christian Democratic Party, has also extended his condolences.
"Today we join with the Coptic community in mourning the loss of his Holiness Pope Shenouda III. For over 40 years his Holiness has faithfully served the Coptic community and provided charismatic spiritual leadership in a time of sectarian tension, political turmoil and religious terrorism", said Rev Hon Fred Nile..
"For decades he has struggled to bring peace, security and justice to Coptic Christians who continue to suffer persecution throughout the Middle East. The Christian Democratic Party regard it a privilege and honour to have had the opportunity in joining his Holiness in that struggle.
"Like the hundreds of thousands that have flocked to pay their respects at St. Mark's Cathedral, Cairo, we too will continue to honour the legacy of his Holiness Pope Shenouda III and do all we can to assist the Coptic community both here and abroad", Rev Nile stated.
Pope Shenouda was consecrated Pope of Alexandria in 1971. Under his leadership, the Coptic Church experienced rapid growth not only in Egypt but in countries with considerable Egyptian immigrant communities, including the United Kingdom, Europe and Australia.
While there were only four Coptic churches in North America at the time of his succession, this has risen to more than 200 today.
US President Barack Obama said in a statement said: "Michelle and I are saddened to learn of the passing of Coptic Christian Pope Shenouda III, a beloved leader of Egypt's Coptic Christians and an advocate for tolerance and religious dialogue.
"We stand alongside Coptic Christians and Egyptians as they honour his contributions in support of peace and cooperation."
It was Pope Shenouda's wish to be buried at St Bishoy Monastery of Wadi al-Natrun in the Nile Delta.
He spent four years under house arrest at the monastery in the early 1980s after criticising the treatment of Copts under the regime of then President Anwar Sadat.
According to Egypt's state television, Bishop Pachomious of the Nile Delta province of Beheira has assumed papal duties until a new pope is elected.