Rev John Suddards suffered multiple stab wounds at the vicarage in Thornbury, Gloucestershire, Avon and Somerset Police said.
The alarm was raised by workmen who arrived at the building yesterday morning and realised it was locked.
Detective Chief Inspector Simon Crisp, who is leading the investigation,
said: "I am in a position to confirm now that body found yesterday in the vicarage was Reverend John Suddards.
"He suffered multiple stab wounds, and therefore this is now a murder investigation.
"A 43-year-old man has been arrested on suspicion of murder."
He appealed for the help of people who live in Thornbury.
DCI Crisp said the 59-year-old reverend had only lived in the village for "a few months", and police "do not have a good understanding of his friends and family at the moment".
He said detectives are appealing to churchgoers to come forward to tell them what they knew about him, who visited him and who he associated with.
"In particular," DCI Crisp said, "I would be keen to speak to anybody who saw the reverend after 12.30pm on Monday.
"Please don't let it rest on your conscience if you know something and you haven't told us, however small."
The news has sent shockwaves through the clergy and the close-knit community, which lies about 11 miles north of Bristol.
Locals said the St Mary's vicar had only recently taken up his post. According to the parish website, he began the role last July.
The Bishop of Tewkesbury, the Rt Rev John Went, told journalists outside the church: "I was deeply shocked as the Bishop of Tewkesbury and deeply saddened to hear about John's death in such tragic circumstances."
He said he had been due to meet Mr Suddards this morning to review his ministry after the first few months of his time in this diocese.
The bishop spoke at a eucharist service at St Paul's church in Thornbury this morning, where he reminded parishioners they were "part of a fallen humanity where tragic events happen".
The tiny church in a country lane on the edge of the town was packed with people, with the service being moved from the larger St Mary's.
He added in his statement this afternoon: "As a diocese we are very keen to be here to support the church community.
"So I was thrilled that I was able to be with the church community this morning for a short act of worship and our concern as a diocese is very much to support the church community but also the wider community of Thornbury as they seek to come to terms with this terrible tragedy.
"Our hearts, of course, go out to John's immediate family and his
close friends and we shall want as a church to offer all the support and love that they will need as they come to terms with their personal loss over the coming months."
A former barrister, Mr Suddards moved to the area in the summer after serving at St Nicolas Church in Witham, Essex, since 2001 and before that at Great Yeldham parish, 20 miles away.
When he took up the post at St Nicolas the clergyman, originally from Yorkshire, spoke of how he joined the priesthood after an accident.
He told the Braintree and Witham Times: "I used to be a barrister
and I had a fairly major road accident and was paraplegic for nine months.
"I was thinking after that and felt strongly that God wanted me to become a priest."
The Ven Geoffrey Sidaway, archdeacon of Gloucester, said: "We came down to Thornbury this morning to bring our support to the church, our community, in shock at the tragic death of their parish priest."
He said Mr Suddards came to the village from the diocese of Chelmsford six months ago.
"He was a person who cared deeply for people and we were all looking forward to an exciting ministry here in Thornbury," the archdeacon said.
"It may, of course, be some weeks or months before a funeral can take place and so the Bishop of Gloucester will be coming to Thornbury on Friday evening for a short service and to show his solidarity to the people of this church and community at what is an incredibly difficult time."
Mr Sidaway said the murder should act as a warning that when clergymen open their churches and homes to people, they become "vulnerable".
He said: "Sadly this event highlights the vulnerable nature of parish ministry in some of our communities today.
"We will, of course, in the coming months continue to bring our care and support in every way we can to the people of Thornbury."
Asked if he thought the murderer could be a member of the parish, he said: "I don't have that at all.
"But many clergy on a daily basis open their homes and their churches to people and clearly that can put them in a vulnerable situation."
PA
