The left-back has been attracting interest from Atletico Madrid, who have been trying to put a deal in place to take him to the Wanda Metropolitano.
Llorente, 24, was born in Madrid and came through Real's academy as a teenager.
Real Madrid and Atlético Madrid have agreed a deal which will see Marcos Llorente join up with Diego Simeone next season. However, the tide reversed after Zinedine Zidane returned to the helm at Real Madrid in the second half of the campaign.
Rodri had been contemplating a move away from Atletico since the end of the season.
But, with Zidane not really favouring him during his time as the Real Madrid manager, it had always been rumoured that Llorente would end up leaving the La Liga giants this summer.
He also made a handful of games in the Champions League, as Los Blancos failed to defend their title after winning three crowns on the bounce.
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Chelsea have priced Marcos Alonso out of a return to Spain with Atletico Madrid.
The 24-year-old midfielder is primed to replace Spain global Rodri, who is said to be on the brink of a switch to Premier League champions Manchester City.
"The 24-year-old Spanish midfielder will sign on a five-year contract".
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Spanish football star Marcos Llorente has on Thursday, June 20, completed a summer move to Atletico Madrid from rivals Real Madrid.