Astronomers estimate the Tau Ceti planets to be two to six times bigger than Earth.
One of them, with five times the Earth's mass, lies in the star's "habitable zone".
Also known as the "Goldilocks zone", this is the orbital region that is neither too hot nor too cold to allow liquid surface water and, potentially, life.
Details are to appear Astronomy & Astrophysics.
Scientists found the planets using combined data from more than 6,000 observations from three telescopes.
They used the radial velocity method which looks for "wobble" in a star's movement caused by the gravitational tug of planets.
Dr James Jenkins, of the University of Hertfordshire, UK, said: "Tau Ceti is one of our nearest cosmic neighbours and so bright that we may be able to study the atmospheres of these planets in the not-too-distant future.
"Planetary systems found around nearby stars close to our sun indicate that these systems are common in our Milky Way galaxy."