The guidance, called Choosing Bishops, seeks to bring Church policy up to speed with the Equality Act.
It sets down in writing what has been Church practice for some years by stating that openly gay clergy can become bishops so long as they are celibate.
"A person's sexual orientation is, in itself, irrelevant to their suitability for episcopal office or indeed ordained ministry more generally," it reads.
"It would be wrong if account were taken of the fact that a candidate had identified himself as of gay sexual orientation.
"As a matter of law, however, the [Equality] Act allows Churches and religious organisations to impose a requirement that someone should not be in a civil partnership or impose a requirement related to sexual orientation [according to the nature of the office]."
It then reiterates previous guidelines issued by the Church of England which draw a distinction between homosexual activity and homosexual attractions.
"These make it clear that someone in a sexually active relationship outside marriage is not eligible for the episcopate or other ordained ministry
"There is, by contrast, no corresponding statement of the position of the Church of England that declares that a celibate person in a civil partnership cannot be considered for appointment as a bishop."
A Church of England spokesman warned against "sensationalised" media reports, advising clergy to read the document "carefully".
The guidance has been issued ahead of the General Synod as information but will not be debated by Synod members when they meet in York next month.
Julian Mann, evangelical blogger and vicar of the Parish Church of the Ascension, Oughtibridge, said the guidance was "significant".
"It is significant that the bishops are making this statement at this juncture," he said.
"It is very important that the Church of England is absolutely clear on the teaching of the Bible: that no communicant Christian should engage in sex outside of lifelong, monogamous, heterosexual marriage."