Rev Galloway was described as an "inspiration, companion and role model" by the community in a statement released by the Community via the Church of Scotland.
In its statement, the Community said she had passed away on Tuesday, following a recent cancer and sepsis diagnosis.
The Churches Together in Britain and Ireland (CTBI) organisation, of which she was a trustee for many years, said it had received the news of her passing "with great sadness".
Ordained in 1977, she first started work with the Church in Edinburgh and became co-Warden of Iona Abbey in the 1980s.
Also serving as the editor of the community's 'Coracle' magazine in the 1990s, Rev Galloway took became the first woman elected as Leader of the Iona Community in 2002, serving until 2009 and then again in the 2010s.
An accomplished author, she published 16 books on topics as diverse as Christian theology to social justice for women and the poor. She also published volumes of her own poetry.
In 2009, she became Head of Christian Aid in Scotland, a role which she held for seven years.
Former Archbishop of Canterbury Dr Rowan Williams looks through sale books with (Left) Loretta Minghella Christian Aid Director and (Right) Kathy Galloway of Christian Aid Scotland. (Image: Stewart Attwood) The Community said: "We grieve with her loved ones the passing of their mother, sister, grandmother, friend.
"And we mourn with the world the loss of a truly prophetic voice of faith for justice, peace and the radically urgent transformation of unjust structures.
"Kathy was an inspiration, companion and role model not only for the wider world, but also of course for so many of us in the Iona Community."
The statement added: "She influenced thousands of people with her compassion, radical voice for justice, wise words and powerful leadership.
"Her poetry and prose writing, widely shared, speaks eloquently of the pain, passion and purpose of life on God's good yet oh so fragile Earth.
"Even from her hospital bed, Kathy remained fully engaged in the launch of PalCafe in Glasgow to support the people of Palestine. Her voice and her actions for justice will live on."
It concluded: "Kathy's death will be mourned by many around the globe including dear friends in the Church of Scotland, Christian Aid and Church Action on Poverty.
"For her life and her witness we give thanks to God as we now bless her on her last journey."
In a statement, the CTBI said: "The ecumenical work to which she has contributed is too numerous to give a comprehensive summary, but we remain indebted to her for her leadership in several areas.
"Kathy challenged us, supported us and led us in bold and courageous paths. We mourn her passing, send our deepest condolences to her family and friends, and remain privileged to have shared Christian discipleship with her."