The 22-year-old defender officially signed from Sampdoria on Friday, signing a five-year deal with the Nerazzurri after a reported €18m transfer fee.
“I could never have expected this,” Skirniar said at his presentation Press conference.
“Two years ago I was at Zilina, now I’m at Inter.
“It’s amazing for me. I talked to my agent and we decided to come to Inter, this is a top club with a great history.
“Everyone at Sampdoria told me the same thing: Inter is a great club.
“[Coach Marco] Giampaolo taught me so much about Italian football, he really helped me and I improved thanks to him. I want to thank the boss and Sampdoria.”
Skriniar also confirmed that this season’s objective is to return to the Champions League.
“Inter deserve a stage like that and we hope to reach the top.”
The defender went on to add that he has already being talking to Inter manager Luciano Spalletti.
“I spoke to the coach on the phone a week ago and he said he was happy to be able to work with me. Now we’ll get the chance to know each other better.
“I don’t know if I’ll be a regular starter – that’s up to him to decide. I have to work hard to improve as a player and then we’ll see how it goes.
“My ex-team-mates told me about Inter’s history and tradition. We need to make sure we’re up there challenging at the top again this season.”
At the age of 22, Skriniar still has much time on his side to develop further and, as he acknowledges, it isn’t a certainty that he will go straight into Inter’s starting line-up.
Having joined Sampdoria in January 2016, Skriniar went on to produce some excellent displays for the club and was especially impressive last season as he averaged seven defensive actions per game and retained possession rather well, completing 92% of the passes that he attempted.