Launching the initial US$100 million phase of the 'Starshot' mission at the One World Observatory in New York City, Hawking said: "There are no greater heights to aspire to than the stars.
"What makes human beings unique? There are many theories. Some say it is language or tools, others say it is logical reasoning. They obviously haven't met many humans.
"I believe what makes us unique is transcending our limits. Gravity pins us to the ground, but I just flew to America. I lost my voice but I can still speak. How do we transcend these limits? With our minds and our machines.
"The limit that confronts us now is the great void between us and the stars but now we can transcend it, with light beams and light sails and the lightest spacecraft ever built we can launch a mission to Alpha Centauri within a generation."
The mission relies on building the lightest spacecraft ever flown - a tiny 'nanocraft' weighing less than a gram which would be fitted with a small sail.
Back on Earth a huge array of laser beams will be fired up into space, coming together to form a 100 gigawatt beam of light which will blast the tiny craft off into the solar system, accelerating to speeds of 96 million km/h.
Although Voyager One has ventured outside the Solar System, and is currently in interstellar space, no spaceship has ever reached another star system.
Speaking at the press conference Milner said: "The question is, can we reach the stars? Can we literally reach the stars? And can we do it in our lifetime.
"The Moon still marks the furthest human beings have come. Since then we have delegated the task to robots. Voyager One has now reached interstellar space. Is that as far as we can go and what will be our next great leap?
"If Voyager had left our planet when humans left Africa it would be arriving at Alpha Centauri about now. So how do we go faster?
"There is a technology just over the horizon which can get us to the speed we need. Actually we already use come of the basic principles. Leave the fuel behind. It was not possible before, but it is possible in the near future.
"If this comes to fruition it will tell us as much about ourselves as about Alpha Centauri. For the first time in human history we can do more than just gaze at the stars. We can actually reach them."
The laser beamed from Earth will be so bright that it will visible throughout the Universe. The team are hoping it might be seen by an advanced civilisations.
"Starshot will answer the question are we alone?" said Pete Worden Executive Director, Breakthrough Starshot, former Director of Nasa Ames Research Centre.
"We can search for intelligent life across the universe. This is really cool. Through these hard challenges, onto the stars."
In 2012, a planet of a similar size to Earth was spotted orbiting the star Alpha Centauri B. Although it is too hot for life - around 2,200 degrees on the surface - it is likely there are other planets nearby that may be cool enough for water and life.
Last year Hawking and Milner launched a joint US$100 million initiative to hunt for evidence of extra-terrestrial civilisations.
Milner is also funding a prize called Breakthrough Message to come up with the best way to communicate with aliens.
Milner, who was named after Yuri Gagarin, the first man in space, said he was committed to bringing the 'Silicon Valley' approach to hunting for intelligent life in the Universe.
The new announcement was made on the 55th anniversary of Gagarin's first spaceflight.
