The Under-21 international becomes the Premier League champions' fourth signing of the transfer window following the arrivals of Erling Haaland, Kalvin Phillips and Stefan Ortega Moreno.
"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," said the 21-year-old, who was previously a Barcelona youth player.
"To be able to be part of this club is a dream come true for me and something any young player would aspire to."
City's director of football Txiki Begiristain said Gomez was an "exciting young talent".
"We're sure that he will bring additional quality to our squad both in defence and going forward and that he will only continue to develop and improve playing under Pep and his coaches," he said.
Guardiola last week confirmed the impending arrival of Gomez, dismissing the suggestion he would be sent out on loan this season.
The 23-year-old Brazilian had a standout performance in Friday's 2-1 win over 13-time European champions Real Madrid that earned a place in the quarter-finals.
The 20-year-old Spaniard, City's first signing of the summer transfer window, has penned a five-year contract for a reported initial fee of £20.9 million ($27 million).
Goalkeeper Rui Patricio was the hero for Wolves, saving three spot-kicks after their Asia Trophy final against Manchester City went to penalties on Saturday in Shanghai. Wolves won the exhibition tournament 3-2 on penalties after the game against the Premier League champions ended 0-0 after 90 minutes.
Chasing 346 for victory, New Zealand lost an early wicket before Ravindra (97) and Williamson (54) put on 137 to put their team on course and they achieved the target with 6.2 overs to spare in Hyderabad.
French Sports Minister Amelie Oudea-Castera said on Sunday French athletes would be barred from wearing a hijab during the Paris Games to respect principles of secularism.
In a video clip circulated on the “X” platform, the dog appeared on the field in a match between Dorados de Sinola and its host Albergue de Oaxaca in the 11th round of the local league.