The biography by the Rev. Andrew Atherstone of Oxford University quotes letters Welby sent to his parish at Southam, Warwickshire, during the 1990s, The Daily Telegraph reported. The newspaper is to publish selections from the book, "Archbishop Justin Welby: The Road to Canterbury," starting Saturday.
Welby replaced Rowan Williams last month as Archbishop of Canterbury, head of the Church of England and of the worldwide Anglican Communion. He is to be enthroned March 21.
He has an unusual background, having worked as an oil company executive before deciding when he was over 30 years old he had a call to the Anglican priesthood. He became bishop of Durham in 2011.
Welby is from the church's evangelical wing, which generally takes a harder stance on homosexuality. But he has recently warned against homophobia and said he supports civil unions for same-sex couples.
His parish letters express the traditional evangelical view.
"Throughout the Bible it is clear that the right place for sex is only within a committed, heterosexual marriage," he said in one. "Interestingly, all recent research also shows that the children of such a relationship are likely (not always but often) to be happier and more stable."
In the book, Atherstone depicts Welby as a man with a sense of humor about the "episcopal bling" he wore as bishop of Durham, describing himself as looking like a "self-propelled toadstool." But he also had a deep concern for the church and worried about dwindling congregations.
"Big buildings and big institutions fall down slowly, but there comes a point when the roof really does fall in and we move from being Durham Cathedral to Fountains Abbey," he wrote in a memo to his bishop's council, referring to one of the most famous ruins in northern England.
Atherstone's biography is the first to appear since Welby's election to Canterbury.
"He speaks his mind with wonderful frankness, unencumbered by nervous press officers," the author said.