Powell, 50, was in charge of the national team between 1998 and 2013 and also managed the Great Britain side at the 2012 Olympic Games in London.
She was sacked after England's group-stage elimination from Euro 2013.
"I'm delighted to be back in management at a club that has so much ambition with amazing infrastructure both on and off the pitch," Powell said.
"The task is now to build a side capable of mounting a challenge for promotion into FA Women's Super League One."
Amy Merricks will be Powell's number two, with interim boss George Parris reverting to the role of regional talent club technical director.
Paul Barber, Brighton's chief executive, previously knew Powell during his period as the Football Association's commercial director.
He told the club's official website: "Hope has an incredible wealth of coaching experience at the very highest level, and had a very impressive career as a player too.
"This appointment also further demonstrates the ongoing commitment that the chairman, myself and the board of directors have in promoting women's football at the club."
Former England boss Hope Powell has been named manager of Women's Super League 2 side Brighton & Hove Albion.