The 2019-20 champion has departed the DS Techeetah squad following this weekend's season finale in Seoul, and will partner a retained Pascal Wehrlein at the team.
Da Costa initially joined Formula E with the Amlin Aguri squad in 2014, later moving to the Andretti team in 2016 ahead of its tie-up with BMW.
After Lotterer moved to Porsche for the German squad's first season in Formula E in 2019-20, da Costa moved to Techeetah - born from a takeover by Chinese media company SECA of the Aguri team.
He won the title that year in a pandemic-interrupted season with 158 points after winning two of the six Berlin races.
"It's like a dream come true. I'm really looking forward to cracking on and winning races for this team," said da Costa,
"I've been beaten by a Porsche many times in my career, and not only in Formula E, so I know that Porsche does everything to win. It's in the brand's DNA.
"I share the same ambition and can hardly wait to bond with the team and work together to ensure a successful start to the Gen3 era."
Da Costa won just one race in 2021-22, taking the spoils at the second New York race, but was on pole twice - at Marrakech and at the Seoul finale.
He placed eighth overall in the standings, but was just 22 points off teammate Jean-Eric Vergne, who finished in fifth.
"We're very much looking forward to working with Antonio," said Porsche's Formula E director of motorsport Florian Modlinger.
"I know him from various racing series and I have a lot of respect for him on a personal level. It's incredible what he has already achieved in Formula E.
"We'll do our utmost to give him a competitive Gen3 car so that he can fight for wins and titles.
"The team is very much looking forward to welcoming him."
Porsche will become a supplier entity in Formula E for the first time next season too, as it will provide the Andretti team with its Gen3 powertrains.
