The Greek mathematician Pythagoras was the first to propose the idea of a round Earth, primarily based on the behavior of the Earth's shadow on the moon. Aristotle made several arguments for a spherical Earth based on physical evidence, and Eratosthenes used mathematics to prove it and measure Earth's circumference.
While Pythagoras theorized about a spherical Earth, credit for actually discovering the Earth's shape usually goes to Aristotle. Aristotle made a number of arguments to back up his point, such as how ships appear to sink below the horizon and how constellations move differently when observed from different lands. In addition, Greek philosophers were notorious for assigning discoveries to their earliest thinkers, so it's unclear whether or not Pythagoras really made the discovery he is credited with. In any case, by 250 B.C., the Greeks knew the shape of the Earth and its approximate size.