Dominic Grieve said the evidence he killed himself was "overwhelmingly strong" and he had seen nothing to support allegations he was murdered.
Dr Kelly, who was at the centre of a row between the BBC and Labour government over Iraq intelligence, was found dead in 2003.
The inquest was suspended as the Hutton inquiry investigated his death.
Dr Kelly's body was found in woods near his home in Oxfordshire, after he was exposed as the source of a controversial BBC report casting doubt on the government's claim that Iraq had weapons of mass destruction capable of being fired within 45 minutes.
A group of doctors have mounted a long-running campaign for the inquest to be re-opened, claiming the evidence did not point to suicide.
David Kelly Dr Kelly was the source of a BBC report casting doubt on government claims about Iraq's weapons
But Mr Grieve said his department had thoroughly investigated their complaints and could not find any legal basis for referring the case to the High Court, which has the legal authority to order an inquest.
Mr Grieve told MPs: "Having given all the material that's been sent to me the most careful consideration, I've concluded that the evidence that Dr Kelly took his own life is overwhelmingly strong.
"Further, there is nothing I've seen that supports any allegation that Dr Kelly was murdered or that his death was the subject of any kind of conspiracy or cover up."
There had to be some "evidential basis" to refer a case to the High Court, he told MPs, but in this case there was none and it would have been "dismissed" by judges "with what I would assume would be a certain amount of irritation".
He said the Hutton inquiry, which ruled the scientist had committed suicide, was "tantamount to an inquest" and there was not sufficient evidence to warrant a further hearing.
His department has published full medical and pathology reports on Dr Kelly's death, as well as Mr Grieve's statement on why he has decided not to refer the matter to the High Court.
Lord Hutton's report in 2004 concluded that Dr Kelly had killed himself by cutting an artery in his wrist but a group of doctors has since argued there was insufficient evidence to prove beyond reasonable doubt he killed himself.
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In Full: Statement and debate
Asked if his statement would put a stop to conspiracy theories, which one MP claimed were being fuelled by former members of the security services, Mr Grieve said: "The evidence overwhelmingly shows Dr Kelly committed suicide. He wasn't killed by anybody."
Mr Grieve offered his "sincere sympathy" to Dr Kelly's family, "not simply for their loss, great though that undoubtedly is, but for having to bear that loss in the glare of intrusive publicity over such a long period of time".
"While I realise that it will always be impossible to satisfy everyone, I would hope for their sakes that a line can now be drawn under this matter."
But the doctors campaigning for an inquest said they were "perplexed and outraged" with the decision.
A statement issued by their leader, Dr Stephen Frost, accused the government of being "complicit in a determined and concerted cover-up". They will now seek a judicial review of Mr Grieve's decision.
"These matters are of such juridical and constitutional importance that the campaign will continue unabated," they said.
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The attorney general has rejected calls for an inquest into the death of government scientist Dr David Kelly.
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