The 38 year-old midfielder had announced his departure on Friday before Del Nido Carrasco made his public proposal.
And this morning, Navas said in a statement: "I didn't hesitate for a second to accept the proposal of the president of my Sevilla FC. I want to continue playing for my Sevilla. I am happy to accept the possibility of continuing to be associated with the club that I have fallen in love with.
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"My wish, and I told the president this, is to continue playing until December to help the team. At that time I will decide to hang up my boots and wear the shirt that I have always dreamed of, that of a Seville player.
"And one more thing: for the next few months, my last as a professional footballer, I will not receive a salary. The salary agreed with the president will be donated to a foundation."