The Frenchman became Roberto Mancini's first signing for the Eastlands outfit on Friday on an initial six-month contract from Inter Milan, with the likelihood it will be extended by a further year should all parties be in agreement.
And for Vieira, it is just the same feeling as the one he got when he first arrived in north London and began to work with Gunners boss Arsene Wenger as he said: "I can see similarities with Arsenal. You can feel the excitement around the people who are working for the club. It is there with the fans and, of course, there is the ambition of the players."
He added: "I met the directors and they really want to take the club somewhere they have never been. They have a fantastic project and the future looks really bright.
"Hopefully, together we can achieve something this club deserves."
And, while it has been revealed Blues owner Sheikh Mansour is looking for a top-four spot this year and the Premier League title next term - a timescale generally regarded as ambitious - Vieira wants to go even faster.
"When I look at the players this club has got, I strongly believe the league is not out of reach," said Vieira. "I believe we can do it. I am sure we can."
Vieira's arrival has been greeted with a degree of scepticism, largely because the midfielder's best days were thought to be behind him when Wenger turned the penalty he scored in Cardiff to beat Manchester United in the 2005 FA Cup final into his last touch for the club.
Yet, just down the road at another snowy Carrington, Ryan Giggs is proof age is not automatically a barrier to success and - while Vieira accepts he can no longer tear round the field trampling on opponents in the manner of old - equally, he is hardly a geriatric.
"I never had any doubt that I could do a big job here," said the 33-year-old. "I believe in myself. I know that I am not 20. But I am not 45 either. I am very motivated to do well and believe I can be successful."