The 25-year-old Argentina striker had a medical on Wednesday and president Aurelio De Laurentiis later tweeted a photograph of himself with Higuain and Napoli's new coach Rafa Benitez captioned: "On behalf of Rafa and I, welcome Gonzalo!".
The club said on Thursday on their Twitter feed Higuain would be presented to the media at 1730 GMT at the club's training camp in Dimaro, northern Italy.
Higuain's move ends a six-and-a-half year stint in the Spanish capital, where he won three La Liga titles and a Copa del Rey, and he is the third player to move from Real to Napoli in recent weeks following Jose Callejon and Raul Albiol.
Napoli are looking to strengthen their squad for their domestic and Champions League campaigns and had cash to spend after last week agreeing the sale of Uruguay striker Edinson Cavani to Paris St Germain for a reported fee of €64 million (£55m).
Higuain cost them €37m (£31m) plus a possible €3m (£2.5m) more in performance-linked bonuses, while forward Callejon and defender Albiol were around €9m (£7.75m) each, Spanish media reported.
Born in Brest, France where his father was playing professional soccer, Higuain joined Real from Argentina's River Plate in December 2006 but initially struggled to win a place in the starting line up.
He established himself by netting 22 league goals in the 2008-09 season and was the club's top scorer with 27 goals the following year before a back injury sidelined him for most of the 2010-11 campaign.
He scored 22 goals in Real's championship-winning season under Jose Mourinho in 2011-12 but finished with a disappointing 16 in La Liga last term.
Never a favourite of Real president Florentino Perez, who was not in charge of the club when he joined, Higuain was regularly touted as the player most likely to make way for the latest "galactico" signing.
He showed resilience to silence his critics but made clear his desire to leave the nine-times European champions after captaining the side in the final game of last season.
Nicknamed "Pipita" after his father Jorge, who was known as "Pipa", Higuain could have opted to play for France as he holds a French passport.
Diego Maradona brought him into the Argentina squad in the run up to the 2010 World Cup finals, where he finished as his nation's leading scorer with four goals.
- Sports & Recreation
- Rafa Benitez
- Aurelio De Laurentiis