The planets, forming a mini-solar system, circle the star 61 Virginis which is just 27.8 light years away and can be seen with the naked eye.
They have masses ranging from 5.3 to 24.9 times that of the Earth.
Astronomers hope to discover even smaller potentially habitable worlds within a few years.
The same international team also found a fourth planet orbiting another Sun-like star 84 light years away called 23 Librae.
61 Virginis lies in the constellation of Virgo, visible from both hemispheres. It has 0.96 of the Sun's mass and is only slightly less bright.
The star's family of planets was discovered by British, Australian and US astronomers using the Anglo-Australian Telescope in New South Wales, Australia, and the Keck telescope in Hawaii.
The new worlds were identified by measuring the "wobble" effect of their gravity tugging on their parent star, a standard planet-finding technique.
Professor Chris Tunney, one of the astronomers from the University of New South Wales, said: "These planets are particularly exciting. Neptune in our Solar System has a mass 17 times that of the Earth. It looks like there may be many Sun-like stars nearby with planets of that mass or less. They point the way to even smaller planets that could be rocky and suitable for life."
The findings on 61 Virginis are to appear in The Astrophysical Journal. The fourth planet is a Jupiter-sized "gas giant" orbiting 23 Librae in the constellation of Libra. Another planet was found orbiting this star in 2006. It takes 14 Earth-years to circle its star, only slightly more than Jupiter's 12-year orbit.