A High Court judge has decided that former Government chief whip Andrew Mitchell did call Pc Toby Rowland a "pleb" because the officer did not have the "wit, imagination or inclination" to invent it.
Mr Justice Mitting said he had reached the "firm conclusion" that the 58-year-old MP used the "politically-toxic" word in Downing Street that evening in September 2012 when he was not allowed to cycle through the main vehicle gates.
Mr Mitchell, who resigned as whip a month after the altercation, vehemently denied during his two-week libel action against News Group Newspapers (NGN) that he had said: "Best you learn your f****** place - you don't run this f****** government - you're f****** plebs."
He said he would never call a policeman a pleb "let alone a f****** pleb" although he agreed he muttered audibly under his breath 'I thought you lot were supposed to f****** help us' - but not directed at the officer.
But, the judge said the MP was not in a state of mind that evening either to measure his words carefully or remember precisely what they were.
He was satisfied that Mr Mitchell did lose his temper and it was part of common experience of life that loss of temper could lead both to loss of inhibition in speaking and recollection of what was said.
"It follows that his adamant denial of uttering the words alleged is not of itself determinative of the issues."
He concluded: "I am satisfied, at least on the balance of probabilities, that Mr Mitchell did speak the words alleged, or something so close to them as to amount to the same, including the politically-toxic word pleb."
He said that Pc Rowland presented as a rather old-fashioned officer, determined to do his duty, and that was to maintain security in Downing Street by enforcing the cycle policy.
Rejecting the claim that there was collusion by the officers on duty at the gate, he said that Pc Rowland was "not the sort of man who would have had the wit, imagination or inclination to invent on the spur of the moment an account of what a senior politician had said to him in temper".
Mr Mitchell, who was in court with his wife Sharon Bennett, said he was "bitterly disappointed" with the ruling.
Thanking his family and friends for their loyalty and support, he said: "This has been a miserable two years. We now need to bring this matter to a close and move on with our lives."
Pc Rowland, speaking in a personal capacity and not on behalf of the Metropolitan Police Service, said: "I would firstly like to thank Mr Justice Mitting for his judgment, my legal team and my family and friends for their unwavering support through what has been the very worst of times for me personally.
"It is with huge regret that what happened at the gates of Downing Street more than two years ago has ended up here.
"It should be pointed out that I and my team tried everything possible to stop the need for court action."
He added: "Even before this trial began, I had already been cleared of any wrongdoing by four extensive and wide-reaching investigations including a criminal one.
"I am delighted that here again my innocence, integrity and reputation as a police officer has been recognised.
"The pain me and my family have been through is indescribable and it is particularly saddening that all this happened because I was following procedure and simply doing my job without fear or favour.
"I also recognise how difficult it must have been for Mr Mitchell's family and I hope now that a line can be drawn and everyone can be left in peace."
His solicitor, Jeremy Clarke-Williams of Slater & Gordon, said: "Toby has had this dark cloud hanging over him ever since the Plebgate incident.
"It has been put right now. The world cannot dispute that Toby Rowland acted properly that night."
Steve White, chair of the Police Federation of England and Wales, said: "We are pleased that the judge has ruled in Pc Toby Rowland's favour. Toby's name has been cleared and his integrity restored.
"Toby has conducted himself with dignity and professionalism in relation to this incident and subsequent inquiries and legal cases.
"It is important that this incident is now brought to a close to allow Toby and his family to look to the future."
The Sun based its story, which it said was substantially true, on the account given in Pc Rowland's log, which was leaked by others to the paper.
Managing editor Stig Abell said: "Today represents vindication for The Sun and its journalists. We have always stood by our story and continue to do so. We are delighted that the judge has ruled that what we reported about events on Downing Street in the evening in question was the truth and accurate.
"There has been a lot of speculation and comment about Mr Mitchell's outburst, and criticism of our newspaper. The judgment today lays all that to rest. Our article broke this important public interest story, and it has been independently and conclusively confirmed. The Sun can be proud of its journalism today.
"More importantly, today marks a victory for all journalism. We now live in a world where the task of uncovering what goes on in our institutions has never been more difficult. It is the job of journalists to shine light into the dark corners of public and political life. There are many in the establishment who do not want us to do that.
"A meek press does not serve the public interest, only the interests of our political classes. Today, this verdict has endorsed the value of robust and irreverent journalism, and we are delighted at the result.".
The judge directed that Mr Mitchell should have 14 days to tender an undertaking not to repeat the claim that Pc Rowland had fabricated his allegations and for both sides to discuss and agree if possible an order for the further progress of the actions.
If another hearing is necessary, it will take place in the new year.
The costs of the entire litigation were unofficially estimated at £3 million by court sources.
Mr Mitchell was ordered to pay interim costs of £300,000 - to be shared between the Police Federation, which funded Pc Rowland, and NGN - by January 3, but the total bill the MP faces has yet to be determined.