"I'm delighted to be here, back in English football at a club who have made tremendous progress over the last three years," Gregory told the club's official website.
"When I met the directors I was impressed by their ambition to keep on moving Crawley Town forward. You can't stand still in football and the potential at this club is enormous.
"We have got a good squad of players and I have every confidence that they can challenge for the playoffs. You have to aim high and I'm really looking forward to getting on the training ground with the players and kicking on."
Chief executive Michael Dunford added: "We're absolutely delighted to have John on board. He is very experienced in management with a wealth of contacts in the game and, most importantly, he is really looking forward to a new challenge and being back in English football."
Gregory will take charge of his first game on Saturday when Crawley go to Bristol Rovers in the second round of the FA Cup.