Head of football operations David Burke said that the experience of Starkey, who was born in Brighton, having come through the Chelsea ranks will serve the club well.
"We are really pleased to have signed Jesse, not only because he has come through the ranks at Chelsea and because of the training he had there, but also because he is a local lad," Burke told the club's official website.
"Brighton was a centre of excellence when he chose to go to an academy with Chelsea but now we are identifying local talent and attempting to bring them back to our academy.
"Jesse is one of the players who falls under that umbrella, because he is a local boy and we are delighted he has joined the club."
Starkey had previously been on trial with the Seagulls.