Demidov, 25, had been linked with a move to Championship side Wolves to work with fellow Norwegian Stale Solbakken, but the Bundesliga newcomers interjected and offered the Latvia-born centre-back a three-year contract.
"We are very pleased to have been able to bring this transfer to a successful conclusion for Eintracht Frankfurt," Eintracht director of sport Bruno Hubner said.
"We have been able to sign a strong central defender who has leadership qualities and therefore fits into the team profile of Eintracht Frankfurt and head coach Armin Veh."
The former Rosenborg defender joined Sociedad in January 2011 and made 36 Liga appearances. He has 15 caps for Norway.