The first written mention of the village dates back to 1156, where it still appeared under the name Scheuden.
Archaeological research carried out in 1971 showed that the area of the village had been inhabited since the beginning of the Stone Age. The first excavations took place at Busahegy, which became the most significant site — stone tools several thousand years old were found here. Traces of settlement from the 4th millennium BC were also discovered. Notable from the 5th–4th millennium BC are anthropomorphic artefacts — two vase-like vessels interesting for their ceramic form and the idea of identification with the female figure.
In 1427 the village received town privileges and market rights. During the Kuruc wars (1708) both parts of Svodín were occupied by Francis Rákóczi. In 1938–1945 both villages were incorporated into Horthy’s Hungary. After the restoration of Czechoslovakia following the Second World War they again became part of it, and from 28 June 1948 they were merged under the name Svodín.