The England Under-19s international will join the League Two side until the end of the season.
"Sanchez Watt is a player we have monitored and admired for some time now and we are absolutely thrilled that a player of his quality is coming to Crawley," manager Steve Evans told the club's official website.
"He had several offers to go to Championship and League One clubs but he likes the idea of playing for a club who are challenging for promotion.
"I think he can make a really big difference to what is already a very talented squad. I cannot remember being as excited about a signing for some time."
Watt, 20, will be in the squad for this weekend's FA Cup fourth-round tie at Hull City.