Dr Craig, 58, was nominated by 17 out of the 19 presbyteries which met on Tuesday evening throughout Ireland.
He will take up office on 3 June in succession to Dr Roy Patton who will continue as Moderator until that time.
Rev John Dickinson, minister of the Carnmoney congregation received the remaining two nominations.
Commenting on his election Dr Craig said: "Personally I am deeply humbled and honoured to be elected Moderator and am delighted for the congregations and members within the Presbytery of Derry and Strabane and west of the Bann ingeneral for whom this a clear sign of support from the wider Presbyterian Church."
As Moderator Dr Craig will chair the 2013 General Assembly when it meets in his home city of Londonderry from 3 to 6 June.
It's the first time the annual meeting of church leaders will be held outside Belfast for the first time in 22 years, and the first time since in Londonderry since 1933.
Rev Rob Craig is married with two daughters and has been minister of the Kilfennan Congregation in Londonderry since for nearly 20 years.
He describes his ministry as open, welcoming and caring, encouraging people to be good neighbours.
"At Kilfennan we think of ourselves as a church in the community, Presbyterian in our practice, but where we hope to be salt and light to people from all backgrounds," said Dr Craig.
"This is evident from the strong emphasis of the 350 family strong congregation in its weekly programme of activities involving everyone from mums and tots, younger children, teenagers, runningmen's and women's groups and conducting a weekly ministry in a nearby residential home for older people."
Dr Craig was born in Magherafelt and was educated at Armstrong Primary School in Armagh and then Wallace High School in Lisburn.
He attended Lowe Memorial Presbyterian Church in Finaghy.
After completing a BA degree at Queens University, Belfast, he joined the Christian missionary organization Operation Mobilisation and served with them in the Bihar region in the north of India for three years working in street mission and literature distribution.
He completed his training for the Presbyterian ministry at Union Theological College in Belfast gaining a Divinity degree before being ordained in 1983.
After serving as assistant minister in Glengormley, he was called to be minister of the Co Down congregations of Clough and Seaforde in 1985 and nine years later became the minister of Kilfennan.
In 2012 he graduated with a Doctor in Ministry also from Union Theological College.