The 22-year-old Spanish defender arrived at the club from Numancia in the winter break and he has produced a string of impressive displays.
Saavedra agreed a four-year deal earlier in the month and the club were given the green light to complete the formalities on Wednesday when Numancia confirmed the sale.
The young defender has expressed delight at sealing the move, as he said: "I like it very much at ADO Den Haag and so I'm very happy that I can play longer for the club.
"In the Dutch competition there's much more attacking than in Spain and that appeals to me very much.
"ADO have extended the contracts of some supporting players and with the help of our fantastic fans I'm convinced that we can continue the upward curve.
"Besides, with the coming of the new stadium it can only become better."
ADO, meanwhile, are one of three teams to express interest in Feyenoord outcast Gill Swerts.
The midfielder has been told he can leave De Kuip in the summer, news which has seen ADO, Vitesse Arnhem and Utrecht to come forward.
"I have heard these three teams are interested," Swerts told Feyenoord's website. "I will have to talk with them before making a decision."
