Coppell, who has also had stints as manager of clubs including Manchester City, Crystal Palace and most recently Bristol City, takes up his new post with immediate effect.
In a statement, Crawley announced: "Steve will oversee all aspects of the club's football operations. Craig Brewster will remain as caretaker manager."
Former Inverness and Dundee United boss Brewster was handed the temporary job on Monday after Steve Evans left the club to become manager of Rotherham, and steered the League Two team to a win at Barnet to keep them in contention for automatic promotion.
Crawley currently stand fourth, with three teams going up to League One.
Former England and Manchester United winger Coppell, 56, has led both Palace and Reading into the Premier League in his career as a manager, and has been out of the game since leaving Bristol City in August 2010, after less than four months in charge.
At the time, Coppell said he was retiring from managing but hoped to find another role within football.
Crawley chief executive Alan Williams said: "Bringing someone with Steve's stature in football as well as his experience and detailed knowledge of the game to Crawley Town is another important milestone in the development of the club.
"Steve's background and pedigree will help us to achieve our aims of pushing into League One and beyond and I am sure his appointment will be welcomed by everyone with Crawley Town FC at heart."