The Athletic understands Brighton will receive an up-front sum for the left-sided Spanish defender of £56million ($68million), with the prospect of a further £7million ($8.5million) in additional clauses.
They are also signing Chelsea’s central defender Levi Colwill on loan for the season.
No loan fee is involved for the 19-year-old.
Cucurella had been told to stay away from first-team training this week, with head coach Graham Potter keen to avoid any distractions ahead of Sunday’s opening Premier League game against Manchester United.
The 24-year-old Spaniard handed in a transfer request amid interest from Manchester City.
But the reigning Premier League champions pulled out after falling well short of Brighton’s valuation.
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Cucurella joined Brighton from Spanish side Getafe for £15million ($18.25m) last summer.
He impressed for Potter’s side, featuring at left-back, left centre-back and left wing-back over the course of 35 Premier League appearances.
Cucurella scored once for Brighton, against Manchester United. He won Brighton’s Players’ Player of the Season award and their Player of the Season honour.
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(Photo: Getty Images)