The Chilean, 27, trained with Inter on Monday and has joined after a season with Cardiff City in the Premier League.
Medel injured his left quad two days before Chile's World Cup round of 16 loss to Brazil but played 109 minutes before finally succumbing to the injury.
Speaking to Inter's website after training with Walter Mazzarri's side for the first time, Medel – a midfielder capable of playing in defence – said he was looking forward to representing the Milan-based club.
"Yes, I'm finally at Inter and I'm thrilled to be at this great club," he said.
"Very good. I'm doing physical work [running] at the moment.
"I'm working hard and hopefully I'll be ready to play for Inter soon. I'm really happy to have joined a great club where there are lots of great players.
"Hopefully my team-mates and I will be very successful this season."
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