Prof Hawking said the £4.4bn machine, in which scientists are about to recreate conditions just after the Big Bang, is "vital if the human race is not to stultify and eventually die out."
And he sought to ease fears that the machine could have apocalyptic effects. "The world will not come to an end when the LHC turns on," Prof Hawking said, adding: "The LHC is absolutely safe."
Scientists at the CERN research centre in Switzerland are aiming to use the machine to gain a better understanding of the birth and structure of the universe, and to fill gaps in our knowledge of physics.
They hope that by recreating the moments after the Big Bang - the massive explosion thought to have created the universe - the experiment will make clearer what the universe is made of, what makes it expand and also to predict its future.
Prof Hawking, the Lucasian Professor of Mathematics at the University of Cambridge, said: "The LHC will increase the energy at which we can study particle interactions by a factor of four."
However, he doubts that the machine will have the power to unravel some of the universe's more elusive secrets such as the putative Higgs boson particle - thought to have given mass to all other particles.
Prof Hawking said he has placed a bet of $100 that the scientists won't find the Higgs boson - the so-called "God particle."
"Another discovery that we might make is superpartners, partners for all the particles we know ... they could make up the mysterious dark matter that holds galaxies together," he told BBC Radio 4.
"Whatever the LHC finds or fails to find, the results will tell us a lot about the structure of the universe," Prof Hawking added.
However he dismissed speculation that the world could be put in grave danger by the force of the experiment.
"The LHC is absolutely safe. If the collisions in the LHC produced a micro black hole - and this is unlikely - it would just evaporate away again, producing a correctoristic pattern of particles," he said.
"Collisions releasing greater energy occur millions of times a day in the earth's atmosphere and nothing terrible happens. The world will not come to an end when the LHC turns on."
However he pointed out that if the LHC were indeed to create minor black holes, his own work on the subject could be verified and he chould receive the highest acclaim in the field.
He said: "If the LHC were to produce little black holes, I don't think there is any doubt I would get a Nobel Prize, if they showed the properties I predict.
"However I think the the probability that the LHC has enough energy to produce little black holes is less than 1 per cent - so I'm not holding my breath."
Asked whether the results of the LHC experiment would offer immediate practical benefits for our day-to-day lives, Prof Hawking urged patience.
He said: "Throughout history, people have studied pure science from a desire to understand the universe, rather than practical applications for commercial gain. But their discoveries later turned out to have great practical benefits.
"It is difficult to see an economic return from research at the LHC, but that doesn't mean there wont be any."
Prof Hawking made clear that the LHC project is one of the most important in the history of scientific endeavour. Asked to choose between it and the space program, he said: "That is like asking which of my children I would choose to sacrifice.
"Both the LHC and the Space program are vital if the human race is not to stultify and eventually die out. Together they cost less than one tenth of a per cent of world GDP. If the human race can not afford this, then it doesn't deserve the epithet 'human'."