The system, known as a circumbinary planetary system, is 4,900 light-years from Earth in the constellation Cygnus, NASA said in a statement.
The discovery proves that more than one planet can form and persist in the stressful realm of a binary star and demonstrates the diversity of planetary systems in our galaxy.
Measurements of the star's orbits from McDonald's Observatory showed that daylight on the planets would vary by a large margin over the 7.4-earth-day period.
Astronomers detected two planets in the Kepler-47 system, a pair of orbiting stars that eclipse each other every 7.5 days from our vantage point on Earth.
One star is similar to the sun in size, but only 84 per cent as bright. The second star is diminutive, measuring only one-third the size of the sun and less than 1 percent as bright.
"In contrast to a single planet orbiting a single star, the planet in a circumbinary system must transit a 'moving target.' As a consequence, time intervals between the transits and their durations can vary substantially, sometimes short, other times long," said Jerome Orosz, associate professor of astronomy at San Diego State University and lead author of the paper.
The binary star is called Kepler-47. The primary star is about the same mass as the sun, and its companion is an M-dwarf star one-third its size.
The inner planet is three times the size of earth and orbits the binary star every 49.5 days, while the outer planet is 4.6 times the size of earth with an orbit of 303.2 days.
The outer planet is the first planet found to orbit a binary star within the "habitable zone," where liquid water could exist and thus create a home for life.
However, the planet's size (about the same as Uranus) means that it is an icy giant, and not an abode for life.
The combination of observations from the NASA mission and McDonald Observatory allowed astronomers to understand the characteristics of Kepler-47's two stars and two planets.
