The 16-year-old attacking midfielder moves to the Spanish capital from Stromsgodset in his homeland and will be presented by his new employers at a Thursday press conference.
Odegaard became the youngest player to represent Norway last year, aged 15, and a statement released on Real's official website on Wednesday evening [local time] confirmed their much-anticipated capture of one of European football's most sought-after talents.
The statement read: "Real Madrid C. F. and Stromsgodset Fotball have reached an agreement for the transfer of Martin Odegaard.
"After undergoing a medical exam, the player will hold a press conference with the director of Institutional Relations, Emilio Butragueno on January 22 at 1:30pm [local time] in the Ciudad Real Madrid press room."
Premier League trio Manchester United, Liverpool and Arsenal were among the clubs linked with a move for Odegaard, while Bayern Munich chairman Karl-Heinz Rummenigge last month claimed he was confident the player would join the Bundesliga champions.
"We will try very hard to sign him and I think we have a good chance," Rummenigge told Bild.
Odegaard made 23 appearances for Stromsgodset in Norway's top flight in the 2014 season, scoring five goals.
