Celtic are understood to be close to signing Belgium goalkeeper Logan Bailly from Oud-Heverlee Leuven.
Doncaster have signed midfielder Richard Chaplow on a two-year contract.
Medel’s future was plunged into doubt at the end of last season following Cardiff City’s relegation from the Premier League.
He admits he had a number of options to consider but insists his preference was always to link up with Inter.
The 27-year-old was given the opportunity to fulfil his dream when the two clubs agreed on a fee, reported to be worth around £10million, and he is now determined to make the move a success.
"I am very happy to be here, I thank the club and my team-mates who have welcomed me very well,” Medel said at a news conference to officially present him as an Inter player.
“There were other teams interested in me, but I always wanted Inter Milan. I hope to help make history with Inter and to win so much with this shirt.”
Medel played for Sevilla before joining Cardiff and is looking forward to competing in another of Europe’s leading competitions.
“Serie A is a big league like the Spanish and the English ones,” he said.
“I want to do better than last season.”