Liverpool agreed a £111m deal for the 21-year-old Ecuador player on Friday.
But Caicedo’s preference is Chelsea and they have finally succeeded with a bid after having a succession of proposals rejected by Brighton this summer.
The fee means Chelsea will break the British record twice in 2023, following the £107m purchase of Argentina midfielder Enzo Fernandez in January.
Caicedo, who was left out of Brighton’s squad for their season-opening win at home to Luton Town, is still to have a medical.
It is understood the initial fee is £100m, with half of the additional payments said to be easily achievable, while Brighton have also negotiated a sell-on clause.
Brighton had set a fee in excess of £100m for Caicedo this summer and said they felt no-one would reach it. Chelsea are believed to have bid £80m previously.
In his news conference before the Seagulls’ game against Luton, manager Roberto de Zerbi said he had “already forgotten” about Caicedo, adding: “Bigger clubs can buy our players but they can’t buy our soul or spirit.”
Caicedo joined Brighton from Ecuadorian side Independiente del Valle for £4m in February 2021, although he did not make his Premier League debut until April 2022.
He asked to leave Brighton in the January transfer window earlier this year and Arsenal had multiple offers turned down for the midfielder before he signed a new contract until 2027 in March.
Caicedo will be Chelsea’s eighth signing of the summer, following Axel Disasi, Christopher Nkunku, Nicolas Jackson, Lesley Ugochukwu, Angelo Gabriel, Robert Sanchez and Diego Moreira.
New manager Mauricio Pochettino has been tasked with overhauling the squad and vastly improving on last season’s 12th-place finish in the Premier League.
Mateo Kovacic, Edouard Mendy, Kalidou Koulibaly, N’Golo Kante, Mason Mount, Kai Havertz, Christian Pulisic, Ruben Loftus-Cheek, Ethan Ampadu, Pierre Emerick-Aubameyang, Abdul Rahman Baba and former captain Cesar Azpilicueta have all departed so far this summer.
Chelsea opened their Premier League season with a 1-1 home draw against Liverpool on Sunday.
