The Chile international swapped the Bluebirds for the Nerazzurri and sealed a £6m move to San Siro recently.
"Yes, I'm finally at Inter and I'm thrilled to be at this great club," he told reporters. "Very good. I'm doing physical work 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."
The 27-year-old established himself as a prominent figure for Cardiff last season after securing a club record £11m from Sevilla last summer.
However, Medel, who played 34 Premier League games in his brief spell in the Welsh capital, was unable to save the club from relegation.