The 17-year-old winger will officially become a Seagulls player in January 2024, subject to all regulatory approvals.
Speaking to the club's official website, technical director David Weir said: "Adrian is a player we have been watching for a while, and we are now looking forward to him joining us next year.
"We have reached an agreement with Constanta, and we will watch his progress through until January and then decide on his next steps."
Mazilu enjoyed a breakthrough year with SSC Farul during the second half of last season, scoring seven goals in 14 starts across all competitions as the Marinarii won their first-ever top flight title.
The 6ft 1in winger is currently managed by Romanian legend Gheorghe Hagi at SSC Farul and recently played 70 minutes in the club's 1-0 first-leg win over Sheriff Tiraspol in the Champions League first-round qualifiers.
Mazilu has represented Romania at all youth team levels from Under-15 to Under-21 and he most recently played for his country at this summer's European Under-21 Championships.
Brighton are understood to have fended off competition from Serie A trio Roma, Fiorentina and Bologna to win the race for the signature of Mazilu, who has been tipped to become a "top player" by Romanian legend and former Tottenham Hotspur forward Gheorghe Popescu.
Speaking to reporters via ProSport, Popescu said: "I would like his path to be an upward one, to continue the good path, he also has incredible physical qualities, an incredible sense of goal! He has what it takes to be a great striker.
"It is the profile of a big team player, an attacking team. He has speed, he has physicality, he has a sense of goal, he has the necessary ingredients to become a top player."
Brighton boss Roberto De Zerbi has made four signings so far this summer, with Joao Pedro, Bart Verbruggen, James Milner and Mahmoud Dahoud all joining the club on permanent deals.