Navas was one of Costa Rica's standout performers at the recent World Cup, as Jorge Luis Pinto's men exceeded all expectations by topping Group D and reaching the quarter-finals.
Levante president Quico Catalan confirmed last week that his club were in talks with Real over a potential transfer.
And the European champions have now completed the formalities of the deal.
A statement on their official website read: "Real Madrid CF and Levante UD have reached an agreement for the transfer of the player Keylor Navas, who is linked to the club over the next six seasons.
"The player will be presented on Tuesday, August 5, at 13:00 (local time) at the Bernabeu, after undergoing the relevant medical examination."
Navas, 27, impressed as Levante's first-choice goalkeeper last season, having previously played second fiddle to Gustavo Munua at the Valencia-based club.
During the World Cup, he kept clean sheets against England and Italy, before also remaining unbeaten for 120 minutes against the Netherlands, who ultimately saw off Costa Rica in a penalty shoot-out to reach the semi-final.
Navas was one of three nominees for the Golden Glove in Brazil, eventually losing out to Germany's Manuel Neuer, and his arrival at the Bernabeu casts further doubt over the future of long-serving goalkeeper Iker Casillas.
The long-time Spain number one has been linked with a move away from Madrid in the close-season, with Carlo Ancelotti reportedly keen to offload Casillas or fellow shot-stopper Diego Lopez to make room for Navas.
Navas’ former club Levante expressed their gratitude to the outgoing keeper.
"From Levante UD we want to thank him for his professionalism and wish him the best of luck in his new career," read a club statement.
"At the express request of Keylor Navas and Levante UD, and with the consent of Real Madrid, the goalkeeper will attend the city of Valencia in the coming days to say goodbye to the fans."
