The Chile international, who made four appearances for his country at the World Cup, arrived at San Siro from south Wales on a four-year contract following his former club's relegation from the Premier League.
And during his presentation on Monday, Medel is in no doubt a move to Milan was the right choice.
"I am very happy to be at Inter," he said. "I spoke to Pinilla [Medel's compatriot Mauricio, who plays in Serie A with Genoa] who told me Inter are a big club.
"I'd like to thank everyone that brought me here, my team-mates have given me a warm welcome.
"There were other teams in for me, but I always wanted a move to Inter and I'm here at last. I'm ready to play."
Medel was compared by the Italian media to former Milan midfielder Gennaro Gattuso, but the 27-year-old played down any similarities and revealed he had spoken to coach Walter Mazzarri about his plans.
"I'm Gary Medel and I want to show what I can do, perform well and win here at Inter," he added.
"I've already talked to Mazzarri, but what was said will remain between us."
Inter kick off their Serie A campaign at Torino on Sunday, but must first defend a 3-0 lead in the second leg of their UEFA Europa League play-off against Stjarnan on Thursday.
