Kelly was last seen when he left home near Abingdon, north of London on Thursday afternoon after telling his wife he was going for a walk, two days after facing a grilling by a parliamentary committee investigating the affair.
"We can confirm that the body matches the description of Dr Kelly. The body has not been formally identified," a police spokeswoman said.
The family contacted the police when he did not return home late in the evening.
A close friend of Kelly said on Friday Kelly's wife had seen he was under massive strain.
"She told me he had been under considerable stress, that he was very, very angry about what had happened at the committee, that he wasn't well, that he had been to a safe house, he hadn't liked that, he wanted to come home," television journalist Tom Mangold told ITV News.
The government has said it believed Kelly may have been the source of a May report by the defence correspondent of the British Broadcasting Corporation Andrew Gilligan that accused officials of hyping intelligence to justify war.
The BBC and Gilligan are refusing to disclose their source and Kelly had denied the government's allegations.
The report led to parliamentary hearings on how the Blair government made its case for the conflict and caused a row with the BBC.
Andrew Gilligan broke the story
for the BBC
In hearings on Tuesday, Kelly admitted speaking to Gilligan before his report, but said he did not believe he was the source for the accusations.
In his report, Gilligan claimed Alastair Campbell, the government's director of communications and key Blair aide, had ordered that the claim that Iraq could deploy chemical or biological weapons in as little as 45 minutes, be inserted into the government dossier released last September.
Gilligan also pointed out that while the government described the dossier as original, much of it had been derived from a 12-year-old PhD thesis.
That dossier was used by the British government to support the US decision to wage war against Iraq in March.
Hours before the body was found, opposition Conservative MP Richard Ottaway who was on the committee said it would be a "tragedy of ghastly proportions" if "political machinations" had resulted in Kelly's death.
"The political ramifications, if the body is Dr Kelly ... are serious. People are beginning to get edgy about the government and losing their faith in it. People don't trust it any more," Ottoway said.
"And now that political machinations have actually, or could have, resulted in the death of a potentially important person in this whole thing, I don't think will help the government one iota," he said.