Dr Mukarji's 12 years at the helm of the humanitarian agency were celebrated at a service of thanksgiving on Monday.
In a letter read by International Development Secretary Douglas Alexander, Mr Brown praised Dr Mukarji for being "central in keeping justice and the fight against poverty at the top of the political agenda".
He cited Jubilee 2000 and Make Poverty History as just two examples of Christian Aid's reach and influence.
"I know that your work at Christian Aid will have changed, improved and saved the lives of thousands of people whom you will never meet but who will remain forever indebted to you."
The Prime Minister went on to praise Dr Mukarji and Christian Aid for continuing to campaign on the devastating impact of climate change for poor communities around the world.
"It was your work that helped to link development and climate in a way that no person and no agency had managed to do before. The world owes you a great deal in this regard," he said.
In a video message, Dr Williams thanked Dr Mukarji for his "wonderful work" in the last 12 years.
He said: "We have a great deal to be proud of in Christian Aid, the churches' agency for development."
The service at St John's Church, Waterloo, in central London, was attended by supporters and staff of Christian Aid.
The sermon was preached by the Rt Rev John Gladwin, former Bishop of Chelmsford and former Chair of the Board of Christian Aid.
He said: "It is not often that we can say that the communities of poor and marginalised have been given hope because of the work of one man, but that is what you got when you appointed a prophet as director of Christian Aid."
Dr Mukarji encouraged Christian Aid staff to keep up their passion for social justice and a world without poverty.
"For us as Christians, that is a vision of the Kingdom of God," he said.
"The work of Christian Aid, day after day after day, is about people who are not often in the room and who are not often at the table.
"It's about people who have been genuinely disempowered because of their caste or their ethnicity of their gender or their location or their other factors that we do know that keep people excluded or marginalised.
"That is what has kept me in my work - and must keep Christian Aid going."
Succeeding Dr Mukarji is Loretta Minghella, who takes over as Christian Aid director next month.