Asensio, a midfielder who has also attracted interest from Barcelona, will remain at Mallorca on loan until the end of the season and possibly next term as well, the Balearic Islands side said on their website.
Neither club disclosed financial terms but local media reported Real had agreed to pay just under 4 million euros (3.14 million pounds) to secure the player's services.
A Mallorca native, Asensio made his first-team debut in October, 2013 and scored his first goal for the club in March.
(Reporting by Iain Rogers, editing by Toby Davis)
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