One star hosts two planets and the other hosts the third.
The system represents the smallest-separation binary in which both stars host planets that has ever been observed.
The findings may help explain the influence that giant planets like Jupiter have over a solar system's architecture, researchers said.
"We are trying to figure out if giant planets like Jupiter often have long and, or eccentric orbits," said Johanna Teske from Carnegie Institution for Science in US.
"If this is the case, it would be an important clue to figuring out the process by which our solar system formed, and might help us understand where habitable planets are likely to be found," said Teske.
The twin stars studied by the group are called HD 133131A and HD 133131B. The former hosts two moderately eccentric planets, one of which is, at a minimum, about one and a half times Jupiter's mass and the other of which is, at a minimum, just over half Jupiter's mass.
The latter hosts one moderately eccentric planet with a mass at least 2.5 times Jupiter's.
The two stars themselves are separated by only 360 astronomical units (AU). One AU is the distance between the Earth and the Sun.
This is extremely close for twin stars with detected planets orbiting the individual stars.
The system is even more unusual because both stars are "metal poor," meaning that most of their mass is hydrogen and helium, as opposed to other elements like iron or oxygen.
Most stars that host giant planets are "metal rich." Only six other metal-poor binary star systems with exoplanets have ever been found, making this discovery especially intriguing.
Teske used very precise analysis to show that the stars are not actually identical "twins", but have slightly different chemical compositions, making them more like the stellar equivalent of fraternal twins.
This could indicate that one star swallowed some baby planets early in its life, changing its composition slightly.
Alternatively, the gravitational forces of the detected giant planets that remained may have had a strong effect on fully-formed small planets, flinging them in towards the star or out into space.
"The probability of finding a system with all these components was extremely small, so these results will serve as an important benchmark for understanding planet formation, especially in binary systems," Teske said.
The finding was published in The Astronomical Journal.