It will be the Chilean’s third spell in Spain having previously played for Real Sociedad for eight years and spending two seasons at Barcelona.
The 37-year-old signed for Man City in 2016 and played in two Premier League title-winning squads.
Betis finished five points above the relegation zone last season with the second-worst defensive record in the league.
The conceded 60 goals in 38 matches; only relegated Real Mallorca (65) leaked more.
