Today we know that the concept of the spherical Earth dates back to the ancient Greeks, at around the 6th century BC. Nevertheless, it remained only in the philosophical field until the 3rd century BC, when Hellenistic astronomy established the Earth's spherical shape.
It is not clear who discovered first that the Earth is round - and how. Many believe that the discovery was made by the fact that things at the distant horizon (such as a ship or a mountain) disappear from bottom up. Others believe that it was the observations from travelers who noticed that starts change their position in the night sky from place to place. This assumption becomes stronger taken the great number of the Greek colonies around the eastern Mediterranean Sea.
The first time that a real demonstration proved that the Earth is round, was by Ferdinand Magellan and Juan Sebastian Elcano's famous circumnavigation (1519"121521)