Having spent the last four months of the season on loan at Highfield Road, the Icelander sorted out his contract with German side VFL Bochum in order to sign for City.
Mike McGinnity said: "I’m delighted that Bjarni has accepted our offer to rejoin the Club. He did well for us during his time at Highfield Road last season and we hope that form continues into the new campaign. "We are also in contract negotiations with other players and hope to announce more good news in the coming weeks."