The 25-year-old shot-stopper will undergo a medical examination to seal the move to Stamford Bridge.
Kepa Arrizabalaga currently occupies the number one spot, but Sanchez will rival him for the position between the sticks.
The departure of Edouard Mendy, who left for Al-Ahli in the Saudi Pro League last month, forced Chelsea to enter the market for a new keeper.
Sanchez will reunite with former Brighton goalkeeping coach Ben Roberts.
The duo previously worked together, and Roberts will hope he can raise Sanchez’s levels after a drop in form.
He lost his starting role to Jason Steele in March following the arrival of manager Roberto De Zerbi.
Sanchez was left out of Brighton’s squad for their pre-season tour of the United States, leaving his future in doubt.
Brighton have already secured the services of Dutchman Bart Verbruggen from Anderlecht to replace Sanchez.
Negotiations between Chelsea and Brighton remain ongoing over the potential signing of Moises Caicedo.
Brighton have rejected several offers for the midfielder as they want £100m, but Chelsea don’t want to go that high.
Talks for the Ecuadorean will continue, but Chelsea have identified Tyler Adams from Leeds United as an alternative. Ajax’s Edson Alvarez is another option.
After securing a new goalkeeper, Chelsea’s next most pressing need is a defensive midfielder.
They are light in that department, and adding another top-class option is crucial to their hopes of success this season.
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