Stones' name appeared earlier in City's official Champions League squad admitted to European football governing body UEFA on Tuesday, thus confirming the completion of the transfer, reports Efe.
Afterwards, the English side announced the signing and welcomed Stones to the team. He earlier played for Everton.
Stones, 22, signed a contract for six seasons with Spanish coach Pep Guradiola's side.
"It's an ambitious club with a great manager so I can't wait to get stuck in," the player said.
"I know it will be tough getting a place in this team but I'm determined to become the best player I can be and help us to success," he added.
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