Caicedo generated huge interest from Chelsea and Arsenal during the January transfer window, with the Gunners having a £70m bid rejected.
That prompted Caicedo to ask for his way out although Brighton refused to budge.
The 21-year-old Ecuadorian international has only made 29 Premier League appearances since joining Brighton from Independiente del Valle in 2021.
A statement on the club's official website reads: "Moises Caicedo has committed his long-term future to the Albion by agreeing a new contract that runs until 2027, with a club option for an extra year."
Head coach Roberto De Zerbi spoke on the news: "This is a fantastic news for the club, our fans, for me and most importantly for Moises. It will make us stronger as we move forward towards our targets on the pitch."
Brighton are eighth on the Premier League table and are into the quarterfinals of the FA Cup, where they will face Grimsby.
Caicedo starred for Ecuador at the 2022 World Cup in Qatar, scoring once in the tournament.
