Potter was Chelsea's first managerial appointment following the Todd Buhle takeover, but was sacked after less than seven months in charge.
The Blues paid more than £21m in compensation to Brighton, with Potter impressing after leading the Seagulls to 15th, 16th and ninth place finishes in the Premier League in a three-year spell.
Potter, who also coached at Ostersunds FK and Swansea City, oversaw a record £323m spending at Stamford Bridge in the January 2023 transfer window, but success did not materialize and he was sacked after an 11th defeat in 31 matches.
When asked if he felt he had something to prove, Potter replied: “When I hear [Pep] Guardiola says he has something to prove, which we all do.
“In professional sports, you have something to prove every day, and that moves you forward,” he said.
“I'm comfortable with who I am, what I've done, and obviously no one is perfect, life is about accepting successes and accepting setbacks and defeats.
“I think I'm a better person and a better coach for the experience.”
He was also linked to coaching the England national team before Thomas Tuchel, his predecessor at Chelsea, was appointed to succeed Gareth Southgate.
In an interview with The Telegraph, Potter said club football was “more beneficial” than international management.
Potter's first assignment will be against West Ham in the FA Cup third round against Aston Villa on Friday, before they return to Premier League action at home to Fulham on Tuesday.
Former Stoke City boss Narcisse Bilac is part of Potter's backroom staff, joining as first-team coach, with Bruno Saltor appointed as assistant coach and Billy Reid also named first-team coach.
