Navas played his final game in defeat at Real Madrid on Sunday.
Ramos played with the former midfielder with Spain and also over two spells with Sevilla.
And the free agent posted to social media: "Jesus, my friend, my little brother, my son, my family. It's hard to say goodbye to you as a footballer , because you represent everything we all want to be.
"We met in the lower ranks of our Sevilla, we grew up together, we suffered together, we made our debuts together… we fulfilled our childhood dreams together. We met again in the National Team, always hand in hand, and we continue fulfilling impossible dreams together. World Cup, Euro Cup, the success we never imagined with the friendship we always had.
"You triumphed in England, but there is no place like home. And when it seemed that we were going to say goodbye from a distance, we met again. Returning to Sevilla was very special for many reasons, and you were one of them.
"The farewell to the Pizjuán last weekend, the tears of emotion for what we experienced and the sadness of not being able to repeat it again, was that of Sevilla, but it is that of football (as seen today at the Bernabéu) and it is mine.
"The greatest joy is knowing that you will continue in my life and I in yours. Football is a better place thanks to people like you.
"You are loved, my friend Jesús Navas."