Silva, 34, spent a decade with City and made his final appearance as a substitute in Saturday’s 3-1 defeat by Lyon in the Champions League quarter-finals. He is expected to join his new Sociedad team-mates in the coming days for pre-season training.
The 2020/21 La Liga campaign is scheduled to begin on September 12. Sociedad finished sixth last season to qualify for the Europa League.
Silva won 11 domestic trophies in his time in Manchester and is widely regarded as one of the Premier League’s finest imports.
City said a statue will be erected next year in his honour, while a pitch at the club’s training ground will also be named after him.
Silva is the fourth-highest goalscorer in Spain’s history and sixth for all-time appearances and was part of the squads which won the 2010 World Cup and two European Championships, in 2008 and 2012.
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