The particle has been the subject of a 45-year hunt to explain how matter attains its mass.
Both of the Higgs boson-hunting experiments at the LHC see a level of certainty in their data worthy of a "discovery".
More work will be needed to be certain that what they see is a Higgs, however.
Prof Stephen Hawking tells the BBC’s Pallab Ghosh the discovery has cost him $100
The results announced at Cern (European Organization for Nuclear Research), home of the LHC in Geneva, were met with loud applause and cheering.
Prof Peter Higgs, after whom the particle is named, wiped a tear from his eye as the teams finished their presentations in the Cern auditorium.
"I would like to add my congratulations to everyone involved in this achievement," he added later.
"It’s really an incredible thing that it’s happened in my lifetime."
Prof Stephen Hawking joined in with an opinion on a topic often discussed in hushed tones.
"This is an important result and should earn Peter Higgs the Nobel Prize," he told BBC News.
"But it is a pity in a way because the great advances in physics have come from experiments that gave results we didn’t expect."
The CMS team claimed they had seen a "bump" in their data corresponding to a particle weighing in at 125.3 gigaelectronvolts (GeV) – about 133 times heavier than the protons that lie at the heart of every atom.
They claimed that by combining two data sets, they had attained a confidence level just at the "five-sigma" point – about a one-in-3.5 million chance that the signal they see would appear if there were no Higgs particle.
However, a full combination of the CMS data brings that number just back to 4.9 sigma – a one-in-two million chance.
Prof Joe Incandela, spokesman for the CMS, was unequivocal: "The results are preliminary but the five-sigma signal at around 125 GeV we’re seeing is dramatic. This is indeed a new particle," he told the Geneva meeting.
Atlas results were even more promising, at a slightly higher mass: "We observe in our data clear signs of a new particle, at the level of five sigma, in the mass region around 126 GeV," said Dr Fabiola Gianotti, spokeswoman for the Atlas experiment at the LHC.
Peter Higgs joined three of the six theoreticians who first predicted the Higgs at the conference Prof Rolf Heuer, director-general of Cern, commented: "As a layman I would now say I think we have it."
"We have a discovery – we have observed a new particle consistent with a Higgs boson. But which one? That remains open.
"It is a historic milestone but it is only the beginning."
Commenting on the emotions of the scientists involved in the discovery, Prof Incandela said: "It didn’t really hit me emotionally until today because we have to be so focussed… but I’m super-proud."
Dr Gianotti echoed his thoughts, adding: "The last few days have been extremely intense, full of work, lots of emotions."
A confirmation that this is the Higgs boson would be one of the biggest scientific discoveries of the century; the hunt for the Higgs has been compared by some physicists to the Apollo programme that reached the Moon in the 1960s.