The 20-year-old has been a regular fixture in the Betis first team for the past two seasons, with his form during that time drawing the interest of a number of Europe's top clubs.
Ceballos's performances in helping Spain to the final of this summer's Under-21 European Championships only increased the clamour for his signature, with the likes of Barcelona and Juventus also understood to be tracking him.
However, Marca reports that Real Madrid have now agreed terms with the midfielder in a deal thought to be worth around €18m (£15.9m).
Ceballos is understood to have agreed a six-year contract with the Spanish and European champions, and the switch is expected to be officially confirmed by the club on Monday.
Ceballos scored two goals and created two more in 30 La Liga appearances last season.