Their 3-0 defeat to Napoli this afternoon practically sealed their fate, but they had to wait until this evening for confirmation.
Salernitana have 31 points and Cagliari 29, with a totally even head-to-head record, but the Sardinians have a superior overall goal difference.
Genoa were promoted back up in 2007 in the same summer as Napoli and Juventus, staying in the top tier for 15 consecutive campaigns.
The Grifone are the oldest professional football club in Italy, originally founded in 1893.
Genoa won nine Serie A titles, including the very first in 1898, but the most recent was in 1924, effectively before the tournament took the form it has today.
They also lifted the Coppa Italia trophy in 1937 and the Anglo-Italian Cup in 1996.