The 26-year-old Dutchman will join the Royals on a free transfer from Russian side Alania Vladikavkaz after agreeing a two-year contract at the Madejski Stadium with the option of a further year.
The move is subject to international clearance from the Russian football authorities and Alania.
Drenthe joined Real from Feyenoord in 2007 and was loaned out to Goodison Park in 2011, scoring three goals in 21 appearances for David Moyes's side.
The one-time Holland international moved to Russia in February but could not help Alania escape relegation.
He is the Royals' second signing of the summer, joining full-back Wayne Bridge, as manager Nigel Adkins plots an immediate return to the Premier League.