The 21-year-old Spaniard arrives as a replacement for Oleksandr Zinchenko, who joined Arsenal, and becomes City’s fourth summer signing, after Erling Haaland, Kalvin Phillips and Stefan Ortega Moreno.
City turned their attentions to Gomez, who has signed a four-year contract at the Etihad Stadium, after they were reluctant to pay Brighton’s asking price for Marc Cucurella, who instead signed for Chelsea in a deal that could cost £62million.
Gomez provides cover for Joao Cancelo and Pep Guardiola suggested last week that he will not try and bring in another left-back.
Gomez said: “I am incredibly proud and happy to have joined Manchester City. City are the best team in England and in Pep Guardiola I have a chance to learn and develop under the most outstanding manager in world football.
“To be able to be part of this club is a dream come true for me and something any young player would aspire to. The number of trophies City have won over the past few years has been incredible and the style of football the team plays under Pep is the most exciting in Europe.”
Gomez thanked former City captain Vincent Kompany, who was his manager at Anderlecht, for converting him from an attacking midfielder to a full-back.
He added: “Everything started with a call from Vincent Kompany. He told me he thought I could play as a left-back last season. When he told me, I was a bit surprised, but I saw him so convinced that his decision gave me confidence as well to bet on the project at Anderlecht.
“I’m very grateful to him for giving me the opportunity. Now I’m playing as a left-back and I love it. Kompany learnt a lot at Manchester City with Pep Guardiola to become a coach afterwards. He used to play a very offensive style at Anderlecht, so I could spend a long time attacking and providing goals and assists.”
Gomez, who faced his new team-mate Phil Foden in the 2017 Under-17 World Cup final that England won, has taken the No. 21 shirt that David Silva used to wear. He revealed he had a City shirt with his fellow Spaniard’s name and number on as a boy and added: “He was one of my favourite players as a kid.”