The 18 year-old joins the Bees on a 12-month deal with an option for another year after successful extended trials this past summer.
Picotto did his preseason with Brentford B and impressed enough to win a contract.
Brentford B head coach Sam Saunders told the club's website: “Luca has settled in really well since coming on trial with us and he’s made a very positive impression on both the staff and the players. He has demonstrated his quality throughout his trial, training with intensity and working hard in games.
"He is a reliable player who adds healthy competition to what is already a very strong squad, and that will only push his team-mates further. His attitude has been spot on and he shows a real desire to keep improving every day.
"We’re looking forward to continuing to work with him and helping him take the next steps in his development.”