The Chile international says he always had his heart set on a move to San Siro and has shrugged off comparisons with former AC Milan star Gennaro Gattuso
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 [Genoa's Mauricio] Pinilla, 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 AC Milan midfielder Gennaro Gattuso, but the 27-year-old maintains he is very much in his own mould as a player.
"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 Europa League play-off against Stjarnan on Thursday.