"The player will be presented on Tuesday ... on the VIP tribune at the Santiago Bernabeu stadium after undergoing the necessary medical examination," Real said on their website.
Levante also confirmed the deal and thanked Navas for his contribution and professionalism since he joined the Valencia-based club in 2011.
Neither club disclosed financial details but Spanish media reported Real had agreed to pay 10 million euros (7.9 million pounds) for Navas, in line with the buyout fee in his Levante contract.
Known as the "Falcon of Costa Rica" for his agility, Navas was one of the top players at the World Cup finals in Brazil and his brilliant form helped the central American nation unexpectedly reach the last eight.
The 27-year-old was hailed last season as the world's number one keeper by Joaquin Caparros, who was Levante coach at the time, and his arrival at Real is likely to signal the departure of Diego Lopez.
It will also increase the pressure on captain Iker Casillas, who has been under fire in recent months after a series of errors and a woeful World Cup showing when holders Spain failed to advance beyond the group stage.
Navas's performances last season, including a series of memorable duels with Real forward Cristiano Ronaldo, prompted the official La Liga website to proclaim him "the league's best" ahead of the likes of Victor Valdes of Barcelona and Atletico Madrid's Thibaut Courtois.
A modest and quietly-spoken character with deeply held religious beliefs, Navas spent his first year in Spain playing for second division Albacete before Levante came calling.
"Fast, with great reflexes, always well positioned and very secure in one-on-one situations, Keylor Navas has all the attributes of an exceptional goalkeeper," Real said.
"He showed this in Brazil, where he only conceded two goals in five matches and with his saves thwarted nations of the calibre of the Netherlands, England and Italy."
(Reporting by Iain Rogers, editing by Ed Osmond)
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