Potter has signed a two-and-a-half-year contract, replacing Julen Lopetegui, who was axed after just six months in the job.
Potter returns to management for the first time since his sacking by Chelsea in April 2023.
"It's a proud day to be head coach of this amazing club, big tradition, big history, big expectations, big challenge," Potter said.
"I'm really excited, it's a bit like Christmas – Christmas for the adults. Excited, not the best of sleeps last night just from excitement.
"I'm looking forward to meeting the players today, meeting our supporters and getting going."
Potter also said, "It's been 20 months of a good rest, a good break and you can imagine in that time you speak to lots of people. Lots of conversations with different owners and different directors.
"But it was important that I chose the right option for me at the right time and as soon as I spoke to this club, it just felt right for me.
"It's an amazing club with a tremendous, loyal fanbase that is passionate, knowledgeable, knows their football and what they want. I think it's a good fit.
"My experience is that if you can build a team that is recognisable on the pitch, that the supporters identify with, are proud of and enjoy watching and you get that trust and connection between the players and the supporters, with everybody aligned, that's the key."
On his issues with Chelsea, Potter also insisted: "I'm comfortable with who I am, what I've done and clearly no one's perfect, life is about taking the successes and accepting the setbacks and defeats.
"I think I'm a better person and a better coach for the experience."