Mr Justice Mitting said the Tory MP's behaviour was "childish" and that his version of events was inconsistent with CCTV footage of the row with PC Toby Rowland in Downing Street in 2012.
Mr Mitchell, who may face costs of Â£2m, said he was "bitterly disappointed".
PC Rowland said he and his family had been through "indescribable pain".
"I am delighted to hear again my innocence, my reputation and my integrity as a police officer has been recognised. I hope now that a line can be drawn and everyone can be left in peace," he added.
Mr Mitchell sued News Group Newspapers over a story that appeared in the Sun in September 2012 which claimed he called PC Rowland a "pleb".
Mr Mitchell acknowledged that he had used bad language but maintained he had not used that word.
Giving his ruling, Mr Justice Mitting said: "For the reasons given 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 ordered Mr Mitchell to pay interim costs of Â£300,000 but the total bill he will face is not yet known.
Responding to the verdict, Mr Mitchell said: "Obviously I am bitterly disappointed by the result of the judgment today.
"This has been a miserable two years but we now need to bring this matter to a close and move on with our lives."
However, Stig Abell, managing editor of the Sun, welcomed the verdict, hailing it as "a vindication for the Sun and its journalists - it is a victory for all journalism".
By Robin Brant, BBC political correspondent
His majority is massive, so he's comfy in his Sutton Coldfield seat.
But Andrew Mitchell may have no choice but to go and earn more than the Â£67,060 an MP gets if he is landed with a multi-million pound bill for costs and damages.
David Cameron held on to him in the immediate aftermath of the scandal in September 2012, showing his characteristic loyalty.
As a sign of how highly he was regarded there was talk, even after he'd quit the cabinet, that Mr Mitchell might return to frontline politics with a job in Brussels as the UK's commissioner.
That didn't happen, and hopes of any return are now completely gone.
Outside court Mr Mitchell described the past two years as "miserable".
That misery continues, and the former army officer turned investment banker has the next few months to decide - as do party chiefs - if he will continue as an MP.
The judge gave his verdict after listening to two weeks of evidence from 26 witnesses and considering volumes of documents concerning a 15-second exchange.
Weighing up the competing claims, the judge said 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".
He added that gaps and inconsistencies in PC Rowland's account did not demonstrate he had fabricated his account, as Mr Mitchell's lawyers claimed.
If he was making up his account, PC Rowland would have had to have come up with the words within seconds, according to the judge.
The altercation took place as Mr Mitchell, who was government chief whip at the time, attempted to leave Downing Street via the main gate on his bicycle.
Steve White, chairman of the Police Federation of England and Wales, said he was "pleased" that "Toby's name has been cleared and his integrity restored".
Michael Fabricant, another former whip and fellow Conservative MP who gave evidence during the trial, told the BBC his colleague could have kept his job if he had apologised.
"If only he'd shown a little more humility at the time all this could have been avoided," Mr Fabricant said.
Ex-chief whip Andrew Mitchell probably did call police officers "plebs", a High Court judge has said as he rejected a libel case against the Sun.