The transfer remains subject to international clearance, but the 19-year-old midfielder arrives on the South Coast having won the 2020 Under-20 Copa Libertadores, as well as making his senior debut for Ecuador in October.
Caicedo is one of South America's most promising young talents and was previously linked with a move to Premier League giants Manchester United and also West Ham.
Albion maintained a good relationship with Independiente after signing Billy Arce in 2018. Brighton negotiated themselves into pole-position and completed a deal for a reported £4.5m.
Head coach Graham Potter said, “It’s no secret we have been working to bring Moises to the club, and we are very pleased he is finally here.
“He will need time to settle in with the group, for us to get to know him and vice versa, as well as get up to speed and ready for the demands of the Premier League.
“He has done very well in Ecuador and made his debut for his country just 18. He’s an exciting signing, but it is important we give him time to adjust.”
Technical director Dan Ashworth said, “Moises has had a lot of interest from clubs across Europe, which is understandable given how well he has done.
“He’s been one the recruitment team has been aware of for some time and we are confident he is a player with a very exciting future ahead.
“It has been a complicated transfer, due to the current restrictions, and there has been a lot of hard work across several of the club’s departments to get the transfer completed.
“Moises is still a young player, moving away from his country for the first time, so we allow him the time he needs to adjust and adapt.”
Caicedo came through the youth ranks at Independiente del Valle before making his first appearance for the club in October 2019.
A year later he made his first senior appearance for his country in a 1-0 2022 FIFA World Cup qualification defeat against Argentina.
Just four days later he scored his first international goal in a 4-2 win over Uruguay – he now has four caps to his name.