Sky Sports had revealed that Brighton had agreed a deal with Dallison, who was on scholarship terms at Arsenal having joined from West Ham in the summer.
The 17-year-old has now signed a deal taking him to 2015 with the Seagulls.
"We are absolutely delighted that Tom has chosen Brighton as the next stage of his football development," Brighton's head of football operations David Burke told the club's website.
"The long-term strategy of bringing in players of different ages, in areas we need, is something the recruitment department have been set, and this is another example of a talented player who, for whatever reason, hasn't been able to find a pathway with one of the Premier League's top four or five clubs.
"However, he has seen that pathway here at Brighton and he only needs to look at players like Rohan Ince, Solly March, George Barker, Jake Forster Caskey and Lewis Dunk, to see that players will get the chance to play and train alongside our first team on a regular basis helps progression.
"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."