The versatile, left-sided 24-year-old joined Madrid from Feyenoord in 2007 but struggled to tie down a first-team berth at the Bernabeu and spent last season on loan at Hercules.
Drenthe's deal went through late on along with another season-long loan for striker Denis Stracqualursi from Argentinian side Tigres.
The Toffees did not officially sign the pair until late on deadline day as there were primarily departures from Goodison Park.
Those came in the form of Mikel Arteta, unexpectedly to Arsenal, with Ayegbeni Yakubu set to complete a permanent move to Barclays Premier League rivals Blackburn.
Source: PA
Source: PA