Real Madrid first showed interest in the Ghanaian last winter, only for Granada's asking price — anchored to his €10m release clause — to stall the move at the time.
With Naasei refusing to renew a contract that runs to 2028, and interest from other top-flight clubs failing to materialise into a firm offer, Madrid returned this summer and secured him for a fraction of that figure.
The 21-year-old can play either centre-back or right-back, the versatility that first attracted Madrid's scouting department.
A second Granada player is also close to completing a move to Valdebebas. Rayan Zinebi, who is currently on international duty with Morocco's under-20s at the Mediterranean Games, is reported to have already passed the medical required before signing, with the transfer expected to be finalised imminently.
Both players are initially bound for Castilla, though neither move rules out the pair occasionally training with the first team when circumstances allow.