The Englishman, who has signed a two-and-a-half-year contract at the London Stadium, has been out of management since he was fired by Chelsea in April 2023.
West Ham said in a statement that Potter was a highly sought-after coach who was the "board's unanimous choice".
He takes charge with the Hammers languishing 14th in the Premier League, seven points above the relegation zone, after just six wins in 20 league matches during Lopetegui's six-month tenure.
"Very excited, very proud," Potter said at his first press conference on Thursday. "Proud day to be head coach, manager of this amazing club. Big tradition, big history, big expectation, big challenge.
"I'm really excited. It's almost a bit like Christmas for adults."
Potter, dismissed by Chelsea just seven months into five-year contract, said West Ham felt like a good fit.
"It was important that I think I chose the right option for me at the right time and as soon as I spoke to this club it felt right for me," he said.
"It's an amazing tradition here," he added.
"There's expectation, there's demands, a recent history of success. My experience is if you can build a team that is recognisable on the pitch, that supporters proudly identify with and enjoy watching -- if you get that connection between the players and supporters, everybody aligned."
The 49-year-old's first match will be an FA Cup third round-tie against Aston Villa on Friday, followed by Premier League games against Fulham and Crystal Palace.
'Comfortable in own skin'
Potter had successful spells with Swansea and Brighton before taking over at Stamford Bridge in September 2022.
He was linked with the England job before Thomas Tuchel, his predecessor at Chelsea, was appointed as Gareth Southgate's successor.
Potter was asked on Thursday whether he felt he had something to prove after his disappointing Chelsea stint and his lengthy spell out of the game.
"Professional sport, on one level you've always got something to prove every day," he said. "It drives you forward.
"I'm comfortable in my own skin, I'm comfortable with who I am and what I've done. Clearly no one's perfect and life's about taking the successes and accepting the setbacks.
"I think I'm a better person for the experience, a better coach for the experience, well-rested."
Former Real Madrid and Spain boss Lopetegui replaced David Moyes, who left West Ham at the end of last season after a second spell at the London club.
Under the Scot, they qualified for European competition for three consecutive seasons, winning the Europa Conference League in 2023 to secure the club's first major trophy in 43 years.
West Ham were among the biggest spenders in the Premier League in the summer transfer window but Lopetegui won just one of his first six league games and oversaw several heavy defeats, including a 5-2 loss to Arsenal and a 5-0 drubbing by Liverpool, both at home.
A 4-1 hammering at champions Manchester City on Saturday was the final straw for club chiefs.
Lopetegui was the fifth Premier League manager to lose his job this season, following the sackings of Erik ten Hag (Manchester United), Steve Cooper (Leicester), Gary O'Neil (Wolves) and Russell Martin (Southampton).
