Navas, 27, was linked to several of Europe's biggest clubs after his fine performances for FIFA World Cup surprise packets Costa Rica.
In an interview with Teletica Deportes, Levante vice-president Tomas Perez said Navas was headed to the German champions.
"He's going to one of the best teams in Europe and I'm sure that he's going to enjoy playing there and will be good competition for his new team-mate, [Manuel] Neuer," Perez was quoted as saying.
"We're happy for him, because I think he deserves it as a player and a person. He's earned it, he had a great year and we are happy to have helped him grow in his career."
Perez was unable to confirm if Navas was receiving €2 million of the €10 million Bayern are paying for his services.
Navas was a standout at Brazil 2014, making 21 saves, keeping three clean sheets and conceding just two goals in five games.
