Belgian side Genk were holding out for £8.6million for the Colombian right-back, and Palace have now agreed to pay that total fee including add-ons.
Genk have allowed the 27-year-old to travel to England for his medical, and he is due to fly to London on Friday.
Munoz went on strike from Genk training this week, in a bid to push through the move to the Premier League.
Palace see him as a long-term solution in the right-back position, where Joel Ward, 34, and Nathaniel Clyne, 32, are both out of contract this summer.
Asked last week about Munoz potentially joining Palace, manager Roy Hodgson said “Yes, I’ve seen a video of him. He looks like a good player. I’ve only seen a video of him, but on the video he looked good.”
Munoz is Colombia’s first-choice right-back, and in 148 games for Genk since joining in 2020, he has registered 19 goals and 20 assists.
He has also amassed 22 caps for Colombia since his international debut back in June 2021.