The midfielder has signed a five-and-a-half-year contract with the European champions, who have been linked with the South American for a while.
The 21-year-old - who had been linked with a host of clubs over the past few months and is reported to have snubbed Arsenal to link up with Carlo Ancelotti's men - has featured for Brazil's Under-20 and Under-21 levels
A statement released on Friday said: "Real Madrid and Cruzeiro have reached an agreement for the transfer of the player Lucas Silva, who has signed for the club until June 30, 2020.
"The player will be presented on Monday, January 26, at 13:00CET at the Santiago Bernabeu, after undergoing a medical examination.
"Later, Lucas Silva will go out on to the turf of the Bernabeu with the shirt of Real Madrid and meet the media in the press room."