The move -- reported by ESPN last week -- sees Villarreal pay a loan fee of around €2 million for the 19-year-old and does not include an option to buy.
"Villarreal CF and Real Madrid have reached an agreement for the loan of the Japanese midfielder Takefusa Kubo, who will play for the Yellows for the 2020-21 season," Villarreal said in a statement. "Kubo is a young midfielder who has excellent ball control, and stands out for his extraordinary ability to beat opponents, as well as his excellent reading of the game."
Kubo will form part of a new project under coach Unai Emery, who took over at Villarreal last month.
Villarreal's bid convinced both the player and Real Madrid, offering regular first-team football as well as Europa League experience, after Villarreal's fifth-placed La Liga finish this year.
Real Madrid signed Kubo from FC Tokyo in 2019 on a five-year contract.
The forward was initially set to play for their reserve team Castilla before the club decided he was ready for first division football.
Kubo had previously spent four years with Barcelona at youth level.