She will join the Diocese of Exeter in July before being installed in September.
Dame Sarah, 53, is currently serving as the Canon Treasurer at Salisbury Cathedral and was once the government's Chief Nursing Officer for England.
She left her post as Chief Nursing Officer in 2004 to take up full time ministry, becoming a Team Rector in Sutton, Surrey, in 2006. In 2012 she was installed as Canon Treasurer at Salisbury Cathedral.
She was made a Dame Commander of the British Empire in 2005 in recognition of her outstanding contribution to nursing and midwifery.
She said: "I am delighted to be appointed as the Bishop of Crediton and visit these projects today. These projects show that our communities, inside the Church and out, are built on the love and compassion people have for each other.
"In even our smallest rural communities, often where many of the other services and facilities have long gone, the church – and it can sometimes be only a few people – remains, as a symbol of God's enduring love.
"Throughout my life, as both a nurse and a priest, I have experienced this love and I hope as Bishop to be able to share that love with others.
"My calling as a Christian and now as Bishop has been shaped by my belief that we are called to be witnesses to the generous love of God and the good news of Christ Jesus.
"In my future ministry in the Diocese of Exeter I hope to encourage and enable Christians to grow in their faith, to share that faith with confidence and to serve the people of Devon with joy."
The Bishop of Exeter, the Rt Revd Robert Atwell, said he was delighted to welcome Sarah to Devon.
"This is an outstanding appointment. Sarah will enrich the life of the church in Devon enormously," he said.
"She will bring to her new role the same mixture of compassion, integrity and professionalism that has characterised everything she has done and achieved, both nationally and specifically within the Church of England."
As Bishop of Crediton, she will primarily look after east and north Devon, though in common with the Bishop of Plymouth, she will minister across the whole diocese.
Dame Sarah is the fourth woman bishop to be appointed by the Church of England, and the first in the South West.
She is married to Eamonn and they have two children, aged 23 and 19.