Kelly was born in Rhondda, Wales. He graduated from the University of Leeds with a BSc and subsequently obtained an MSc at the University of Birmingham. In 1971, he received his doctorate in microbiology from Linacre College, Oxford for thesis titled The replication of some iridescent viruses in cell cultures. In 1984, he joined the civil Service working at what is now Dstl Porton Down as head of the Defence Microbiology Division. He moved from there to work as an ad hoc advisor to the MoD and the Foreign Office.

In 1989, Kelly was involved in investigations into Soviet violations of the 1972 Biological Weapons Convention and was a key member of the inspection team visiting the USSR and former Soviet states on several occasions 1991 and 1994. His experience with biological weapons at Porton Down led to his selection as a United Nations weapons inspector in Iraq following the end of the Gulf War. Kelly's work as a member of the UNSCOM team led him to visit Iraq thirty-seven times, and his success in uncovering Iraq's biological weapons programme led to Rolf Ekéus nominating him for the Nobel Peace Prize. He was made a Companion of the Order of St Michael and St George in 1996. Although he was never a member of the intelligence services, the Secret Intelligence Service (MI6) regularly sought his opinion on Iraq and other issues. Kelly became a member of the Bahá'í Faith around 1999. He was introduced to this faith by Mai Pederson, a US military Linguist and intelligence operative.

Although he was not responsible for writing any part of the dossier, Kelly's experience of weapons inspections led to his being asked to proofread sections of the draft dossier on the history of inspections. Kelly was unhappy with some of the claims in the draft, particularly a claim originating from August 2002 that Iraq was capable of firing battlefield biological and chemical weapons within 45 minutes of an order to use them (known as "the 45-minute claim"). Kelly's colleagues queried the inclusion of the claim, but their superiors were satisfied when they took it up with MI6 through the Joint Intelligence Committee.

During the inquiry, British ambassador David Broucher reported a conversation with Kelly at a Geneva meeting in February 2003. Broucher related that Kelly said he had assured his Iraqi sources that there would be no war if they cooperated, and that a war would put him in an "ambiguous" moral position. Broucher had asked Kelly what would happen if Iraq were invaded, and Kelly had replied, "I will probably be found dead in the woods." Broucher then quoted from an email he had sent just after Kelly's death: "I did not think much of this at the time, taking it to be a hint that the Iraqis might try to take revenge against him, something that did not seem at all fanciful then. I now see that he may have been thinking on rather different lines." According to an entry in one of Kelly's diaries, discovered afterwards by his daughter Rachel at his home, this meeting did not take place in February 2003, but in February 2002. According to Kelly's half-sister, Sarah Pape, the day after his daughter's wedding on Saturday 22 February 2003, Kelly flew to New York. Pape told the inquiry that Kelly "certainly did not mention he was going to be flying almost straight back to visit Geneva."

The government immediately announced that Lord Hutton would lead an inquiry into the events leading up to Kelly's death. The BBC shortly afterwards confirmed that Kelly had indeed been the single source for Andrew Gilligan's report. The inquiry took priority over an inquest, which would normally be required into a suspicious death. The Oxfordshire coroner, Nicholas Gardiner, considered the issue again in March 2004. After reviewing evidence not presented to the Hutton Inquiry, Gardiner decided there was no need for further investigation. This conclusion did not satisfy those who had raised doubts, but there has been no alternative official explanation for Kelly's death. The Hutton Inquiry reported on 28 January 2004 that Kelly had committed suicide. Lord Hutton wrote:

The story of Kelly was also the subject of a 2005 television drama, The Government Inspector, starring Mark Rylance, and the impact of his death is one of the themes of Jonathan Coe's 2015 novel Number 11.

The BBC broadcast a programme on Kelly on 25 February 2007 as part of the series The Conspiracy Files; the network commissioned an opinion poll to establish the views of the public on his death. 22.7% of those surveyed thought Kelly had not killed himself, 38.8% of people believed he had, and 38.5% said they did not know. On 19 May 2006 Norman Baker, Liberal Democrat MP for Lewes, who had previously investigated the Hinduja affair, which led to the resignation of government minister Peter Mandelson, announced that he had been investigating "unanswered questions" from the official inquiry into Kelly's death. He later announced that he had uncovered evidence to show that Kelly did not die from natural causes. In July 2006, Baker claimed that his hard drive had been wiped remotely. Baker's book The Strange Death of David Kelly was serialised in the Daily Mail before publication in November 2007. Family members of Kelly expressed their displeasure at the forthcoming publication, the husband of Kelly's sister saying, "It is just raking over old bones. I can't speak for the whole family, but I've read it all [Baker's theories], every word, and I don't believe it." In his book Baker argued that Kelly did not commit suicide and examined the many unanswered questions he says surround the incident.

The death of Kelly and preceding events have served as an inspiration for artistic tributes and dramatisations including the song "Harrowdown Hill" by Thom Yorke and a painting titled Death of David Kelly (2008) by Dexter Dalwood.

On 5 December 2009 six doctors began legal action to demand a formal inquest into the death, saying there was "insufficient evidence to prove beyond reasonable doubt he killed himself." In January 2010, it was disclosed that Lord Hutton had requested that all files relating to his postmortem remain secret for 70 years. In 2010, Attorney General Dominic Grieve was said to be considering an inquiry to review the suicide finding.

In October 2010, the postmortem that Hutton had requested to be sealed for 70 years to protect the Kelly family was made public by the new government. The report by Nicholas Hunt stated: "It is my opinion that the main factor involved in bringing about the death of David Kelly is the bleeding from the incised wounds to his left wrist. Had this not occurred he may well not have died at this time. Furthermore, on the balance of probabilities, it is likely that the ingestion of an excess number of co-proxamol tablets coupled with apparently clinically silent coronary artery disease would both have played a part in bringing about death more certainly and more rapidly than would have otherwise been the case. Therefore I give as the cause of death: 1a. Haemorrhage; 1b. Incised wounds to the left wrist; 2. Co-proxamol ingestion and coronary artery atherosclerosis."

Simon Armitage has published a poem, titled "Hand-Washing Technique – Government Guidelines" and subtitled "i.m. Dr David Kelly", hinting at an internal cover up.

On 29 October 2017 it was reported that Kelly's body had been exhumed at the request of his family. This action was taken due to threats of exhumation by protestors who did not believe Kelly committed suicide. The body was apparently moved and cremated.