The 59 year old has signed an 18-month contract with the League One club and replaces Richie Barker, who was dismissed last week after 15 months in charge.
"I'm delighted to be here, back in English football at a club who have made tremendous progress over the last three years," said Gregory.
"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."
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