
Marca said Barca have agreed to pay 14.25 million euros (21.02 million dollars) for the 21-year-old defender.
Garay has caught the eye in his two seasons at Santander with his defensive solidity, his intelligent positioning and his eye for goal.
Santander are one of the surprise packages of the Spanish season, together with newly-promoted Almeria.
They are sixth in La Liga - their highest ever placing at his stage of the season - and in the semi-finals of the King's Cup for the first time in their modest history.
The purchase of Garay could be the prelude to Barca selling off veteran defenders Lilian Thuram, Gianluca Zambrotta and Sylvinho.