The 17-year-old centre-back has recently been on trial with the South Coast club and impressed enough to earn himself a contract.
Brighton head of football operations David Burke told the club website: "If Tom hits his performance targets he has a realistic chance of reaching the first team, that isn't always the case at many other clubs."
Under-21 coach Simon Ireland, who played Dallison for the U21s against Crystal Palace recently, added: "He is comfortable on the ball, he looks to step in which is something we encourage, and he has got a good range of passing.
"He also has a good physique which is what you want from a central defender and with that a good work ethic. He also seems keen to learn, which is what you want from any young player."
Dallison joined Arsenal from West Ham last season.