The 25-year-old Malta international has made 38 appearances for the Town since signing from Barnet for an undisclosed fee in January 2017. He has found the net three times and helped the Hatters to promotion from the fourth tier last term.
The popular midfielder will link up with Crawley ahead of their game at Oldham tomorrow.
He will be eligible to play for the Sussex club in the FA Cup, but not the Checkatrade Trophy.
Good luck in your time at the Broadfield Stadium, Gambo!