He has agreed a four-year deal and is coming for an undisclosed fee estimated at around £9million.
The 21-year-old Scotland midfielder is available for a game against Leicester on Sunday.
Albion manager Graham Potter said: “Billy comes with a fantastic pedigree, having represented Scotland in the Premier League, Champions League and last year’s Euro. He will complement our existing midfield options.
“This experience at a fairly young age shows the strength of character he has and we’re really excited about his potential.
“Now it’s about giving him the time to get used to a new environment and to settle into our club. We can’t wait to work with him.”
https://www.theargus.co.uk/sport/20884645.brighton-sign-billy-gilmour-chelsea/?ref=rss Brighton sign Billy Gilmour from Chelsea