No financial details of the transfer were given but Italian media reported that the player had cost Napoli some 12 million euros.
Napoli are looking to strengthen their squad for their domestic and Champions League campaigns and had a large pot of cash to spend after agreeing the sale of Uruguay striker Edinson Cavani to Paris St Germain for a reported fee of 64 million euros on Tuesday.
Albiol, a product of Valencia's youth academy where he mainly played as a midfielder, made his debut with the east coast club in September 2003 under new Napoli coach Rafa Benitez.
He had a brief stint at Getafe before joining Real in 2009 but has spent much of his time in the capital on the bench.
Despite his lack of playing time at club level, he kept his place in the Spain squad through the 2010 World Cup and Euro 2012 and has made 40 appearances for the world and European champions.
Albiol's former Real team mate Jose Callejon joined Napoli last week and club president Aurelio De Laurentiis said on Wednesday they were also chasing Real's Argentina forward Gonzalo Higuain.
- Sports & Recreation
- Real Madrid
- Edinson Cavani