The 19-year-old, who has committed his future to the South Coast club until June 2018, has set his sights on achieving promotion to the Premier League.
"I'm really excited; hopefully it's going to be a good four years with the new training ground and the club pushing for promotion," he told the club's official website.
"The staff are working hard behind the scenes to get the best young players and hopefully more of us can come through from the academy to the first team.
"A new contract does bring security, but we've got to keep moving forward. The main aim is to get promotion, so hopefully we can do that in the next few years. Being a Premier League player is the ultimate aim for any footballer, so hopefully we can get there soon."
March has made 23 first-team appearances for Brighton this season, having made his debut in August.