The Basque club have been searching for a replacement for Jagoba Arrasate who paid the price for a dismal start to the season when he was dismissed earlier this month.
Sociedad have subsequently turned to Moyes, who has been out of work since April when his ill-fated tenure at Manchester United was brought to an end less than 12 months into a six-year contract.
The Scot, who has penned a deal at Anoeta until June 2016, was chosen as the successor to legendary manager Alex Ferguson at Old Trafford, but endured a torrid tenure at the club, losing 11 of the 34 Premier League games he took charge of and failing in the UEFA Champions League, the FA Cup and League Cup.
Previously, Moyes enjoyed an 11-year spell in charge of Everton, where he drew plaudits for helping the club achieve consistency in the Premier League.
During his time at Goodison Park he also led Everton to the UEFA Champions League preliminary stages in 2005 and the 2009 FA Cup final.
The 51-year-old will now look to rebuild his reputation as a coach in Spain's top flight, with his first task to help Sociedad - who were also reportedly in talks with former West Brom coach Pepe Mel - climb the league table.
Sociedad currently sit 15th, although they did achieve a morale boosting 2-1 victory at home to champions Atletico Madrid on Sunday.
That victory was just their second league win of the campaign, their first being a shock 4-2 triumph over leaders Real Madrid in August.
