Kubo, 19, impressed last season in his debut campaign in the top-flight on loan at Real Mallorca although was unable to prevent the team from being relegated a year after winning promotion.
The playmaker spent time at Barcelona’s academy but was forced to leave the club due to FIFA’s rules prohibiting the signing of underage players, which led to Barca being hit with a transfer ban.
Sharing the full story, not just the headlines
He signed for Real from FC Tokyo last year for two million euros ($2.35 million) on a six-year contract.
Kubo joins a Villarreal side in the middle of a huge transformation ahead of the new season, having replaced coach Javi Calleja with Unai Emery after finishing fifth last campaign.
The club are also set to sign midfield pair Dani Parejo and Francis Coquelin from neighbours Valencia, according to reports in the Spanish media.