The 24-year-old had a spell on loan with the Reds in 2013 and was released by Luton in March.
Manager Mark Yates told the club website: “We’re delighted to have Luke on board. I think he is a very talented footballer and someone whose career I have followed closely since his days at Swindon.
“He had an injury last year which held him back a bit but I saw him several times for Luton and he was outstanding. A lot has changed at Crawley since his loan spell here but he does know the club and he is really enthusiastic about a new challenge and a fresh start here.
“He has a lot of qualities on the ball and I can see him playing a big part for us.”