Speaking at this week's General Assembly of the Church of Scotland in Edinburgh, Mr Brown said that he shared the Kirk's "enduring vision of the good society".
Reflecting on the extent to which his father, a Church of Scotland minister, had influenced his own views, he said: "He also brought us up to believe that the size of your wealth mattered less than the strength of your character; that a life of joy and fulfilment could be lived in the service of others."
Mr Brown argued that the "consistent ethical core" at the heart of the world's main religions shows "that we are not moral strangers but there is a shared moral sense common to us all".
He issued the call to people in all nations to join together in a "single moral universe to bring about change", particularly in social justice issues.
"This is the irrepressible revolution of our time - a billion voices for change. And I'd like to think that acting together we can become the generation to address climate change," he said.
"Acting together, the first generation in the history of mankind to abolish illiteracy and give every child the right to education; acting together, the first generation to eradicate tuberculosis, polio, diphtheria, malaria, on the way to eradicating HIV/Aids.
"And to honour the dream of the scriptures: that justice will roll like water and righteousness like a mighty stream."
Mr Brown's speech comes 20 years after Lady Thatcher delivered her famous "Sermon on the Mound" address, in which she attempted to argue biblical justifications for her free market zeal to a largely unconvinced General Assembly.
Earlier in the week, the Church of Scotland General Assembly welcomed its new Moderator into office.
Rev David Lunan, 63, who took over from the outgoing Rev Sheilagh Kesting, announced that his year as spiritual representative of the Kirk would centre on the themes of "prayer and money" in light of the huge injustices still prevalent in the modern global economy.
