The 59-year-old former Aston Villa, Derby and QPR boss is back in English football after a six-year absence and takes over a club lying 15th in League One following eight games without a win.
"I'm delighted to be here, back in English football at a club who have made tremendous progress over the last three years," he said.
"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 play-offs.
"You have to aim high and I'm really looking forward to getting on the training ground with the players and kicking on."
Gregory has yet to decide who will be his assistant at the Broadfield Stadium.