The 20-year-old, second cousin to Blackpool winger Thomas Ince, left Stamford Bridge last week and has agreed an 18-month contract with the Seagulls.
Ince has had a spell on trial with Brighton and impressed in reserve matches against Bournemouth and Ipswich.
He told the club website: "It's a positive signing for me as Albion are a very good team with a beautiful stadium.
"The football they play is so similar to Chelsea and I can see myself fitting in. It's always hard leaving Chelsea but I'm very pleased to find this club.
"I knew Albion were a good footballing side, they play out from the back and are in a good competitive position to break into the Premier League within the next few seasons.
"I hope I can perform to a high level within the development squad and then get a chance to prove myself in the first team in the future."