The 19-year-old has emerged as a first-team regular under Oscar Garcia this season and he has been attracting glances from a number of Premier League clubs.
But Brighton have now tied March down to a new four-year deal at the AMEX Stadium.
Garcia was delighted to have finalised the deal and said: "Solly has made great progress this season and deserves this new contract. He has done very well in the matches he has played and has been a pleasure to work with.
"It's hard for any young player to break through into the first team but it is even harder to stay there. That is the next challenge for Solly.
"He has the capability and, if he continues to work hard, I am confident he will achieve that."
March joined Brighton from non-league Lewes in 2011, when he turned down the likes of Arsenal and Newcastle to sign for the Seagulls.