Albion signed Caicedo from Ecuadorian side Independiente del Valle for £4m last January. The 19-year-old midfielder is tipped as one of South America's finest young talents and had attracted interest from Man United, West Ham and AC Milan.
Brighton however were persistent in their pursuit and agreed a four-year contract with the Ecuador international, who made his debut for his country last year in a World Cup qualifier against Argentina and then scored his first international goal in a 4-2 win over Uruguay four days later.
Caicedo has been training with Brighton's first team squad and has greatly impressed head coach Graham Potter who named the youngster in his matchday squad for the 2-1 loss at Manchester United last Sunday.
Caicedo is knocking firmly on the first team door and he will likely get a further chance to impress today as he's set to feature for the under-23s as they host Southampton under-23s in Lancing.
Speaking in his first interview since arriving in the UK, he highlighted Manchester's Paul Pogba and Chelsea's N'Golo Kante as players he admires and learns from.
"I am happy to be at my new club, now I just want to do well," said Caicedo speaking in Spanish.
"N'Golo Kante and Paul Pogba," he said immediately when asked to name his favourite player. "I like the way Kante plays because he pressures a lot and I like Paul Pogba because he has great vision.
"He can provide incredible assists. I learn every day when I watch them. I think it helps watching these top players if you want to carry on improving."
Caicedo is known as an athletic and powerful midfielder and the man who progressed though the youth ranks at Independiente del Valle says he has the discipline and tactical awareness to be a success in the English top flight.
"I would describe myself as a very intelligent player on the pitch. I chose when to attack and when not to.
"I want to settle in as quickly as possible and earn my place in the team because this is my dream to start in the Premier League.
"But this is down to me. I have to train as hard as possible so that I can have a place in the starting XI."
Brighton are six points above the relegationplaces with eight matches of the Premier League campaign remaining. They are next in action on Monday night as they welcome Everton to the Amex Stadium.
Caicedo could once again be included in the squad to face Carlo Ancelotti's unpredictable team.
“Moises has made a really good impression," said Potter. "Both him and Michal Karbownik are going to play for the under-23s in the next few days to carry on that integration and adaptation process into British football.
“It was good for them to be on the bench and get that experience of being around the squad at Old Trafford. We are happy with them, but they need to keep working as well.”