At the end of the campaign Madrid have the option to buy the 22-year-old, who has played for the likes of Sao Paulo and Santos in his homeland.
A Madrid statement read: "Willian Jose da Silva, 22-year-old striker who played in the last Campeonato Brasileiro with Santos, has signed a contract which will see him join Real Madrid Castilla on loan until June of this year. The club reserve the option to buy."
Madrid brought Casemiro to the club from Sao Paulo in similar circumstances last January before signing the Brazilian midfielder on a permanent four-year deal in the summer for a fee reported to be six million euros.
The 21-year-old made his first-team debut for Madrid under Jose Mourinho last season and has featured six times under new boss Carlo Ancelotti this term.