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The findings, published in the journal Nature, show that the planet is located in a distant area of the star known as the "snow line".
This is far beyond the habitable zone where there could be moist water and potentially life, researchers said.
The surface temperature of the planet is estimated to be around 170 degrees Celsius, which means it is likely to be a frozen world that is not detrimental to Earth-like life, they said.
However, if the planet has an important atmosphere, the temperature may be higher and the conditions more welcoming.
"Barnard's star is a famous object amongst astronomers and out-of-plane scientists, as it was one of the first stars where the planets initially claimed, but later proved to be inaccurate." We hope we got it right this time, "said Guillem Anglada Escude of Queen Mary's Physics and Astronomy School.
At nearly six light-years away, Barnard's star is the next closest star to the Sun after the triple Alpha Centauri system.
This is a kind of faint, low-mass star called red dwarf. Red dwarfs are considered the best places to look for candidates for exoplanets, which are planets outside our solar system.
Barnard's star b is the second closest known exoplanet in our sun. The nearest one is just over four light years from Earth.
This exoplanet, called Proxima b, revolves around the red dwarf star Proxima Centauri.
The researchers used the radial velocity method during the observations that led to the discovery of Barnard's star b.
This technique detects rocking in a star that is likely to be caused by the gravitational pull of a planet surrounding the orbit.
These oscillations affect the light that comes from the star.
As the star moves to Earth, its spectrum appears slightly shifted towards the blue and, as it moves away, shifts to red.
This is the first time this technique has been used to detect a planet so small so far from its star.
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