The Serbian centre-back signed on a free transfer after his deal at Manchester United expired and will add experience and quality to Walter Mazzarri's Inter squad.
The 32-year-old was an integral part of United's success in an eight-year stint at Old Trafford but is excited for the next chapter in his career.
And he hailed Inter's size and ambition when speaking to the press on Friday.
"I wanted to join Inter because it's one of the biggest clubs in the world," Vidic said.
"I'm happy to be here. I've always liked the idea of being part of a club with a vision for the future. I'm honoured to be here.
"I spoke to [ex-Inter player and fellow Serb Dejan] Stankovic about coming here. I'm pleased to continue this tradition of Serbian players at Inter.
"English football is a bit different but the Serie A is a big league, I'm looking forward to playing here.
"I nearly came to Italy 12 years ago. I think Italian football is suited to my way of playing.
"I achieved everything at Man United, now I'm here because I want to prove myself again."
Vidic said he had not spoken with ambitious Inter president Erick Thohir yet, but that he had high hopes for the club, and he targeted gradual improvement in his first season with the Italian giants.
"I haven't spoken to president Thohir directly but with [general director] Marco Fassone and [technical director] Piero Ausilio," he added.
"Thohir is enthusiastic and has plans. He wants to take the club back to the position we all want to see it.
"Inter's target? To keep improving, on the pitch, as players and as a club. We'll see where it takes us.
"We won't be in the Champions League but we'll have the Europa League and three competitions to fight for."
