The former Manchester United defender moves to the Primera Division new-boys as a free agent after coming off contract at Villarreal.
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Bailly passed his medical at Oviedo in the morning and has signed a deal to 2027.
The 31 year-old said: "I feel good. There's an important match coming up soon, and I hope to be ready.
"I'm really excited for the team and its history. They achieved something very important with the promotion, and I'm here to give my all."