The new planet is not much bigger than the Earth
The planet orbits the faint star Gliese 581, which is 20.5 light-years away in the constellation Libra.
Scientists made the discovery using the Eso 3.6m Telescope in Chile.
They say the benign temperatures on the planet mean any water there could exist in liquid form, and this raises the chances it could also harbour life.
"We have estimated that the mean temperature of this 'super-Earth' lies between 0 and 40 degrees Celsius, and water would thus be liquid," explained Stephane Udry of the Geneva Observatory, lead author of the scientific paper reporting the result.
London Science Museum
Xavier Delfosse, a member of the team from Grenoble University, added: "Liquid water is critical to life as we know it."
He believes the planet may now become a very important target for future space missions dedicated to the search for extra-terrestrial life.
These missions will put telescopes in space that can discern the tell-tale light "signatures" that might be associated with biological processes.
The observatories would seek to identify trace atmospheric gases such as methane, and even markers for chlorophyll, the pigment in Earth plants that plays a critical role in photosynthesis.
The exoplanet - as astronomers call planets around a star other than the Sun - is the smallest yet found, and has been given the designation Gliese 581 c.
It completes a full orbit of its parent star in just 13 days.
Indeed, it is 14 times closer to its star than the Earth is to our Sun.
However, given that the host star is smaller and colder than the Sun - and thus less luminous - the planet nevertheless lies in the "habitable zone", the region around a star where water could be liquid.
Gliese 581 c was identified at the European Southern Observatory (Eso) facility at La Silla in the Atacama Desert.
To make their discovery, researchers used a very sensitive instrument that can measure tiny changes in the velocity of a star as it experiences the gravitational tug of a nearby planet.
Astronomers are stuck with such indirect methods of detection because current telescope technology struggles to image very distant and faint objects - especially when they orbit close to the glare of a star.
The Gliese 581 system has now yielded three planets: the new super-Earth, a 15 Earth-mass planet (Gliese 581 b) orbiting even closer to the parent star, and an eight Earth-mass planet that lies further out (Gliese 581 d).
Of the more than 200 exoplanets so far discovered, a great many are Jupiter-like gas giants that experience blazing temperatures because they orbit close in to much hotter stars.
The Gliese 581 super-Earth is in what scientists also sometimes call the "Goldilocks Zone", where temperatures "are just right" for life to have a chance to exist.
Commenting on the discovery, Alison Boyle, the curator of astronomy at London's Science Museum, said: "Of all the planets we've found around other stars, this is the one that looks as though it might have the right ingredients for life.
"It's 20 light-years away and so we won't be going there anytime soon, but with new kinds of propulsion technology that could change in the future. And obviously we'll be training some powerful telescopes on it to see what we can see," she told BBC News.
"'Is there life anywhere else?' is a fundamental question we all ask."
Professor Glenn White at the Rutherford Appleton Laboratory is helping to develop the European Space Agency's Darwin mission, which will scan the nearby Universe, looking for signs of life on Earth-like planets. He said: "This is an important step in the search for true Earth-like exoplanets.
"As the methods become more and more refined, astronomers are narrowing in on the ultimate goal - the detection of a true Earth-like planet elsewhere.
"Obviously this newly discovered planet and its companions in the Gliese 581 system will become prominent targets for missions like Esa's Darwin and Nasa's Terrestrial planet Finder when they fly in about a decade."The discovery is reported in the journal Astronomy & Astrophysics.