The body was found at 09:20 BST by a member of the police team searching for Dr Kelly in a wooded area at Harrowdown Hill, near Faringdon, Oxfordshire.
The government has announced that if the body is formally identified as Dr Kelly, an independent judicial inquiry will be held into the circumstances surrounding his death.
Government adviser Dr Kelly, 59, went missing from his home in Southmoor, Abingdon, Oxfordshire, at about 15:00 BST on Thursday.
The body was found lying on the ground, around five miles from Dr Kelly's home, a police spokeswoman said.
Acting superintendent Dave Purnell confirmed that the body matched Dr Kelly's description in a brief news conference at 14:30 BST.
Formal identification would take place on Saturday, said Supt Purnell, and the case was being treated as an "unexplained death".
"We will be awaiting the results of the post mortem and also waiting while the forensic examination continues at the scene at Harrowdown Hill," he added.
The government announcement of an inquiry if the body is Dr Kelly's came from the prime minister's plane as he flew for a visit to Tokyo.
Earlier this week, Dr Kelly denied being the BBC's main source for a story claiming Downing Street had "sexed up" a dossier about Iraqi weapons of mass destruction.
He appeared before the Commons foreign affairs committee on Tuesday.
MPs on the committee reacted with shock and disbelief at news of Dr Kelly's disappearance.
His family had contacted the police when he failed to return home by 23:45 BST on Thursday.
Tony Blair, who is heading to Japan after his speech to Congress in Washington, has been informed about the discovery of the body.
Huge media attention has been on Dr Kelly since the Ministry of Defence said he had admitted meeting Andrew Gilligan, the BBC correspondent behind the controversial Iraq story.
Mr Gilligan said a source had told him that the dossier on Iraq had been "sexed up" by Downing Street.
The BBC correspondent has refused to name his source, but the MoD said Dr Kelly had come forward to say it may have been him.
Government ministers have said they believe he was the source for Mr Gilligan's story.
Superintendent Purnell said the official's family were aware that a body had been found. A police family liaison officer is with them.
Harrowdown Hill, where the body is found, is an area popular with walkers but "quite off the beaten track", he added.
Ann Lewis, a neighbour of Dr Kelly, told BBC News Online she was "devastated" for his family, especially his children.
She said: "He was a quiet man. He was a man who showed great care and concern for others."
Craig Foster, 36, landlord of the Blue Boar public house in nearby Longworth, said Dr Kelly was "a very well liked gentleman".
Police say Dr Kelly is an avid walker and has good local knowledge of the many footpaths surrounding his home.
Initial searches of the house, outbuildings and grounds of the property were completed in the early hours of Friday.
A Ministry of Defence spokeswoman said: "We are aware that Dr David Kelly has gone missing and we are obviously concerned."
The ministry said Dr Kelly had at no point been threatened with suspension or dismissal for speaking to Mr Gilligan.
It was made clear to him that he had broken civil service rules by having unauthorised contact with a journalist, but "that was the end of it", said a spokesman.
Downing Street says it is "very concerned about news that David Kelly has gone missing". A spokesman said thoughts were with Dr Kelly's family.
Number 10 says "normal personnel procedures" were followed after Dr Kelly volunteered that he might have been the source of Mr Gilligan's report.
It was made clear to Dr Kelly that his name was likely to become public knowledge because he was one of only a small number of people it could have been about, the spokesman said.
After questioning Dr Kelly earlier this week, the Commons foreign affairs select committee said it was "most unlikely" he was the main source for the BBC story. And they said Dr Kelly, who has worked as a weapons inspector in Iraq, had been "poorly treated" by the government - a charge strongly rejected by the MoD.
Committee chairman Donald Anderson told the BBC his "heart went out" to Dr Kelly's family as the search for the official went on.
Another member of the committee, Tory John Maples said he was "speechless" after hearing of the discovery of a body. "If it is (Dr Kelly), it is just awful. What can you say? Nothing," he said. "There must be more to this than we had thought. I do not know what that means, I just think there is."
Tory MP Richard Ottaway, another committee member, said: "He is not used to the media glare, he is not used to the intense spotlight he has been put under."
The BBC has rejected Mr Anderson's claim that Mr Gilligan was an "unreliable witness" who had changed his story about the Iraq dossier claims when he met the committee in private on Thursday.
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