Jupiter is the Solar System’s largest planet, which makes its name quite appropriate. So while it isn’t the brightest object in the sky at night, its size makes it visible to the naked eye. Because of this, even the people from the pre-historic period knew that Jupiter existed. Of course, it took a while before they realized what Jupiter was.
Still, the knowledge of its existence before recorded history makes it impossible to know who specifically discovered Jupiter. The credit is given not to the person who discovered its true nature, but to the person who discovered it exists (for instance, the discoverer of Uranus presented it as a comet, not a planet). Therefore, no one gets the credit for Jupiter’s discovery.
Of course, as with the other classical planets, there were astronomers who observed the movement and status of the planet. For instance, Babylonian astronomers observed the planet back in the second millennium—centuries before Galileo Galilee and Nicolas Copernicus discovered the true nature of the planet. The Indian astronomers also observed the planet and wrote the observations in their Surya Siddhanta, credited to astronomer Brahmarishi Mayan. Eastern astronomers also observed the planet and estimated its distance from Earth.
However, it is perhaps Galileo who made the first ground-based research on the planet, thanks to his telescope. Because of this, he was the first to discover the moons of Jupiter. Callisto, Europa, Io, and Ganymede, the Jupiter’s four largest moons, were also called the Galilean moons. All in all, Jupiter has 60 moons and irregular satellites.