The move is subject to Llorente passing a medical at Leeds in a deal that reportedly could reach £18.7million (€20m).
The former Real Madrid centre-back joined Sociedad in 2017 following successful loan spells at Rayo Vallecano and Malaga in La Liga.
A statement issued by his club read: “Real Sociedad would like to thank Diego for the professionalism and commitment shown during the three years that he has been here, at the same time wishing him the best for his personal and professional future.”
Spain international Llorente will likely have to compete with captain Liam Cooper and new signing Robin Koch for a starting place in the centre of defence.
Leeds have three points from their opening two Premier League games, having bounced back from losing 4-3 at Liverpool to defeat Fulham by the same scoreline.
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