"Everett Golson will be our starter against Rice," Kelly said after practice on Wednesday.
Golson returns to his role as starting quarterback for the Irish two years after leading them to an undefeated regular season and a berth in the BCS National Championship game against Alabama as a redshirt freshman.
He was suspended for the fall semester last year, missing the entire season, and was readmitted to Notre Dame in December.
Though Notre Dame never said why he was suspended, Golson implied during an interview with Sports Illustrated that it was because he "had poor judgement on a test."
Asked if he cheated on a test, Golson replied: "Something like that."
Kelly said his decision to start Golson against Rice was made using everything he has seen from the quarterback since January, and not before.
"So (based on) winter workouts, how he handled himself with the team, our workouts, his spring practice and then his leadership in the summer and camp here, he's put himself in position to get that opportunity against Rice," said Kelly.
Golson earned the nod over sophomore Malik Zaire based on his understanding of the offense and his ability to lead, Kelly said.
"There was competition up until I made the decision and there will continue to be competition," Kelly said. "So Everett's the starter for Rice and we hope he's the starter for the entire year but ... just like I tell him, we're all in this merit-based situation. We've got to win. And Everett knows that."
Kelly said he "got the right answer" from Zaire when he told the sophomore of his decision to start Golson.
"He wasn't happy," Kelly said. "If he gave me a hug I'd be very disappointed. ... He's going to continue to work to be the starter."
Golson passed for 2,405 yards and 12 touchdowns in the 2012 season and rushed for 298 yards and another six scores. Senior Tommy Rees started all 13 games at quarterback last season.
Golson said he felt less relief over being named the starter again and more a sense of "heightened responsibility."
"It's my job to get these guys right on offense and just try to lead this team," he said. "You know that you have to go to work now. I have to do my best to prepare for Rice."