Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The 26-year-old Norwegian returns to Spain just five months after leaving Real Sociedad for the Bundesliga, where he failed to command a regular place in the Eintracht first team.
Speaking to Celta's official website at his unveiling, Demidov said: "I'm very happy because I've come to an historic club.
"Hopefully I can stay beyond June 30 and do everything I can to help the team. At a good club like this, players need competition. If there wasn't any, this would not be a great club."
Celta currently sit 17th in the Primera Division table having claimed just one victory from their last 10 league games, with fellow promoted club Real Valladolid next up at the Balaidos.