The 20-year-old was a free agent after leaving Fulham earlier in the summer and has been on trial with the Cod Army since July, even joining them on their pre-season tour of Germany.
Della-Verde spent part of last season on loan with Bristol Rovers in a campaign which culminated in them winning promotion back to the Football League.
“Lyle has been with us since the first day of pre-season. He has shown a fantastic attitude and he brings us something a little bit different in midfield,” Fleetwood boss Graham Alexander told his club’s official website.
“He is a young player with lots of potential. He is hungry for the chance to play first-team football so he is a great addition to a squad that we are already pleased with.
“He is very comfortable on the ball. He can operate in various positions, he is mainly left footed but he is comfortable on his right. He will definitely be a player that will emerge into the first team if not starting. We have high hopes for him.”