The Blancos youth academy product is returning to La Liga after terminating his contract with Serie A outfit Cagliari and is keen to help the club try and avoid relegation
The 26-year-old shot-stopper left Los Blancos for Cagliari last summer only to then terminate his contract with the Serie A side.
Consequently, Adan, a product of Madrid's youth academy, has now decided to return to Spain and join La Liga's basement boys, Betis.
"I am aware of the situation that the club is in but I had to take this bold step," the former Spain Under-21 international told his new side's official website.
"The important thing is to be realistic. The situation is complicated but the bottom line is for us to leave everything on the field, to show all of those people that are behind us that the club will reciprocate that support.
"I have a great motivation to do well, one which I've had throughout my life. My ethos is: work, work and more work."