Stanley will sign a four-year deal worth approximately $1.67 million and will report to training camp in Oxnard, Calif. on time.
The former Louisville standout is expected to compete with Thomas Johnson for the top backup nose tackle spot behind Jason Ferguson.
Cowboys VP of College and Pro Scouting, Jeff Ireland said of Stanley earlier this year, "He's a big, strong guy. He's probably one of the strongest defensive linemen we saw. Pretty good motor. Very strong. Uses his hands. Definitely a 3-4 nose tackle.
"You have Ferguson in there now, and you can't leave him in there every single play. So getting bigger in there was a priority for us."