Cornelius, a former walk-on, was expected to battle incoming freshman Spencer Sanders and Hawaii graduate transfer Dru Brown for the starting job to replace four-year starter Mason Rudolph.
Neither Sanders nor Brown was with the Cowboys during spring practice, leaving Cornelius with the bulk of the first-team snaps.
"When we came out of spring, we felt very comfortable with Taylor," Gundy said Tuesday during Big 12 media days. "He's been with us a number of years, he understands our offense. We're confident in his abilities."
Sanders was the top-rated quarterback recruit from the state of Texas this year. Brown started the past two years for Hawaii, and passed for 2,785 yards and 18 touchdowns last season. As a grad transfer, Brown is eligible this season.
Cornelius has only 24 career passing attempts, completing 15 of them for 220 yards. But he earned a scholarship prior to last season after winning the backup job to Rudolph.
"Taylor is a very intelligent young man," Gundy said. "He's very humble, he understands hard work and he's put his time and effort in."