Moyes, who was axed by Manchester United in April following a dismal first season in charge at Old Trafford, has been handed a contract until June 2016 with the Spanish outfit.
“The Royal Society has reached an agreement with David Moyes to be the first team coach until 30 June 2016,” a statement on Sociedad’s official website read.
Moyes left United just 10 months into a six-year contract after being named as the successor to Sir Alex Ferguson in the summer of 2013.
At the time of his departure, United, the defending champions, were seventh in the Barclays Premier League and 23 points behind leaders Liverpool.
Moyes also left the 20-time title winners with a host of unwanted records broken during his tenure, including failing to qualify for the Champions League for the first time in almost two decades.
Moyes, who became the third shortest-serving manager in the club’s history, won 27, drew nine and lost 15 of his 51 games in charge of United.