The massive galaxy, although mostly shredded, left behind a rich trail of evidence, an almost invisible halo of stars larger than the Andromeda galaxy itself, and a separate compact galaxy M32.
This disrupted galaxy was the third-largest member of the Local Group of galaxies, after the Milky Way and Andromeda galaxies.
Using computer models, Richard D'Souza and Eric Bell of the University of Michigan in the US were able to piece together this evidence, revealing this long-lost sibling of the Milky Way.
Scientists have long known that this nearly invisible large halo of stars surrounding galaxies contains the remnants of smaller cannibalised galaxies.
A galaxy like Andromeda was expected to have consumed hundreds of its smaller companions. Researchers thought this would make it difficult to learn about any single one of them.
Scientists found that even though many companion galaxies were consumed by Andromeda, most of the stars in Andromeda's outer faint halo were mostly contributed by shredding a single large galaxy.
"It was a 'eureka' moment. We realised we could use this information of Andromeda's outer stellar halo to infer the properties of the largest of these shredded galaxies," said D'Souza, lead author of the study published in the journal Nature Astronomy.
"Astronomers have been studying the Local Group - the Milky Way, Andromeda and their companions - for so long. It was shocking to realise that the Milky Way had a large sibling, and we never knew about it," said Bell.
This galaxy, called M32p, which was shredded by the Andromeda galaxy, was at least 20 times larger than any galaxy which merged with the Milky Way over the course of its lifetime.
M32p would have been massive, making it the third largest galaxy in the Local Group after the Andromeda and the Milky Way galaxies.
This work might also solve a long-standing mystery: the formation of Andromeda's enigmatic M32 satellite galaxy, the scientists say.
They suggest that the compact and dense M32 is the surviving centre of the Milky Way's long-lost sibling, like the indestructible pit of a plum.
"While it (M32) looks like a compact example of an old, elliptical galaxy, it actually has lots of young stars. It's one of the most compact galaxies in the universe. There isn't another galaxy like it," Bell said.
The study may alter the traditional understanding of how galaxies evolve, researchers said.
They realised that Andromeda's disk survived an impact with a massive galaxy, which would question the common wisdom that such large interactions would destroy disks and form an elliptical galaxy.