The left-back, who is 21 years old, joins from Anderlecht after making 49 appearances for the Belgian team in the 2021–22 season.
Sergio began his professional career as a member of Barcelona's youth program. At the beginning of 2018, he left the Catalan club to sign with Bundesliga team Borussia Dortmund.
After two loan seasons at Huesca in his native Spain, where he helped the team win promotion to La Liga at the conclusion of the 2019–20 season, he then left to join Anderlecht in the summer of 2021.
Under the direction of former Anderlecht manager Vincent Kompany, Gomez went on to have a strong individual season and was later chosen as the Belgian club's Player of the Year.
Gomez declared, "I am incredibly proud and happy to have joined Manchester City.
"City are the best team in England, and in Pep Guardiola, I have the opportunity to grow and learn from the best coach in football worldwide.
Any young player would hope to join this team, so for me to be able to do so is a dream come true.