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.
‘Newcastle’s board said I was over the hill, so I left and played 108 consecutive games and won the European Cup – not a bad way to answer that accusation!’: Ex-Magpies defender reflects on career highlight after proving former side wrong
‘Parma viewed him as the perfect replacement for Adrian Mutu, who’d left to sign for Chelsea. But Manchester United’s interest was much more concrete’: Cristiano Ronaldo's 2003 transfer details revealed by former Sporting director of football
