The planet circles the faint dwarf star LHS 1140 in the constellation Cetus and lies at the heart of the habitable zone - the orbital band where temperatures are mild enough to allow liquid surface water.
Although it is 1.4 times the size of Earth, its mass is seven times greater, implying a dense world made of rock with an iron core.
Astronomers estimate the planet to be at least five billion years old - about the same age as the Earth and long enough for life to have evolved.
Its star also emits less radiation than many other red dwarfs, making the planet more likely to have preserved an atmosphere.
Lead scientist Dr Jason Dittmann, from the Harvard-Smithsonian Centre for Astrophysics in Cambridge, US, said: "This is the most exciting exoplanet I've seen in the past decade.
"We could hardly hope for a better target to perform one of the biggest quests in science - searching for evidence of life beyond Earth."
The discovery, reported in the journal Nature, was made using the MEarth-South telescope array in Cerro Tololo, Chile, which detected tell-tale dips in light as the planet passed in front of its star.
Follow-up observations studied the star's "wobble" caused by a gravitational tug of war with the planet and confirmed the presence of a super-Earth.
Another Earth-sized planet recently discovered orbiting a second red dwarf 39 light years away could be a steamy "water world", scientists believe.