The 46-year-old Portuguese takes charge at Molineux tasked with reviving the club after their relegation from the Premier League in April, which ended an eight-season stay in the top flight.
Wolves finished bottom with 20 points, managing three wins from 38 matches , scoring 27 goals, and will look to rebuild under Peixoto in the Championship.
"I'm proud to be here at this big, historic club in England. It's a big opportunity for me and I'm prepared to do everything to put Wolves where it belongs in the Premier League," Peixoto said.
"It's a hard-working city with a lot of energy and a lot of passion, and I want them to see a team which plays an offensive game, with good organisation and a team who play for the fans."
Englishman Edwards was axed seven months after quitting Middlesbrough to return to his former club on a three-year deal.
A former Portugal international, Peixoto enjoyed a playing career spanning more than two decades, winning domestic honours and being part of Jose Mourinho's Champions League-winning Porto squad. He moved into coaching in 2019.
He arrives after guiding Gil Vicente to sixth place in Portugal's Primeira Liga last season, his first full campaign in charge of a club.
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