Dr Barr will take up the 12-month leadership role in May 2016.
The 62-year-old, who has been minister Cramond since 1993, and set up Fresh Start more than 15 years ago, said he was “excited, honoured and overwhelmed” to have been appointed.
Reflecting on being chosen to succeed the Right Rev Dr Angus Morrison, Dr Barr said: “It is not a role that I ever imagined being asked to do.
“It is humbling to be elected by your peers to serve the Church in this way.”
He promised: “I will seek to use the role to raise moral and ethical issues and publicise the important part the Church plays in public life.”
Dr Barr, who enjoys golf, rugby, opera and reading in his spare time, said he also hoped to raise greater awareness of homelessness and food poverty - Fresh Start has helped 2,000 people get back on their feet in the last year alone.
He is also very supportive of the Church of Scotland’s Tomorrow’s Calling campaign which is seeking to recruit a new generation of ministers to lead nearly 1400 congregations across the country.
Dr Barr is married to Margaret, a retired secondary school biology teacher, with whom he has a son, Robert, and daughter, Lindsey. He is also grandfather to two.
He is convener of the Presbytery of Edinburgh’s superintendence committee and a member of the business committee, he served as presbytery moderator in 2011-12, was chaplain to the Lord High Commissioner of the General Assembly in 2012-13, and was convener of the Africa and Caribbean Committee of the Church of Scotland’s World Mission Council between 2011-2015.