The League One club, currently 15th, announced Gregory's appointment on Tuesday and the former Aston Villa, Derby County and QPR boss has agreed an 18-month deal.
Barker left his post last Wednesday following 15 months in charge, with Gregory tasked in the short term with halting an eight-game winless league streak.
It is a challenge the 59-year-old is relishing, having been out of work since departing Kazakhstani side Kairat in 2011.
"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 after ending his six-year exile from the English game.
"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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