The 29-year-old enjoyed a successful loan spell in Sussex two seasons ago and has now put pen to paper on a two-year contract.
Crawley manager Richie Barker told the club website: "What I like about Andy as much as anything is his versatility.
"He can play in either central midfield or in wide areas. He has terrific energy and can also weigh in with his share of goals.
"He is coming here for the right reasons. He acquitted himself well in the Championship and wants to play at that level again.
"He's the sort of player I want at the club, someone who is good in possession, works hard and has the right attitude so I'm delighted he's coming to us and I'm sure our fans are too because I know he was extremely popular during his loan spell with us."