Potter was Chelsea’s first managerial appointment following Todd Boehly’s takeover, but dismissed after less than seven months in charge.
The Blues paid more than £21m in compensation to Brighton, where Potter had impressed after leading the Seagulls to Premier League finishes of 15th, 16th and ninth in a three-year spell.
Potter, who has also managed at Ostersunds FK and Swansea City, oversaw a record £323m outlay at Stamford Bridge in the 2023 January transfer window, but success did not materialise and he was sacked following an 11th defeat in 31 games.
He was also linked with the England job before Thomas Tuchel, his predecessor at Chelsea, was appointed as Gareth Southgate’s successor.
In an interview with the Telegraph, Potter said club football was “more rewarding” than international management.
Potter’s first assignment will be West Ham’s FA Cup third-round tie at Aston Villa on Friday, before they return to Premier League action at home to Fulham on Tuesday.