Navarro, who was released by MK Dons in the summer, becomes Slade's eighth new signing of the summer.
Slade told the club's official website: "He's been excellent for us during pre-season and he gives us a different dimension in the midfield.
"He is a very clever player and showed on Saturday (in a 2-0 win over Scunthorpe) just how he can make a team play."
Slade also confirmed Brighton were close to agreeing a deal to sign fellow trialist Jamie Smith on a one-year deal.
The Seagulls boss added: "Jamie has done exceptionally well. He's worked hard to convince us he is worth a contract and he has the potential to be a very good player."