The well-regarded defensive midfielder has come through the ranks at Real and will initially become a member of the U21 squad at Stoke.
A part of the Real youth system since he was just nine, Molina has captained the Spanish side at every level from U10 to U19.
And he impressed in the UEFA Youth League last season, scoring twice in his six appearances.
It was reported last week that Molina had arrived in England for talks and a medical, and the teenager has now finalised his switch.
He follows in the footsteps of fellow Spanish youngster Moha, who arrived at the Britannia from Barcelona earlier this summer.
Molina becomes Stoke’s ninth close-season signing, following the arrivals of Ibrahim Afellay, Philipp Wollscheid, Jakob Haugaard, Joselu, Marco van Ginkel, Glen Johnson, Shay Given and Moha.