"There are certain expectations within our program that must be met on a daily basis," Kelly said in a statement. "Quite simply, Greg did not meet those expectations."
Bryant remains on scholarship and is allowed to practice with the Fighting Irish. His father, also named Greg, told Scout that Bryant is academically ineligible.
Bryant, a redshirt sophomore, was already facing a four-game suspension to start the season because of a violation of team rules, a source had told ESPN.com in June.
The 5-foot-10, 205-pound Bryant had entered Notre Dame in 2013 from American Heritage-Boca/Delray High (Florida) as ESPN's No. 2 running back recruit, but he took a medical redshirt because of knee tendinitis after playing in three games his freshman year. He has played in 15 games for the Fighting Irish, rushing for 303 yards and three touchdowns on 57 carries, and catching five passes for 50 yards. He also has returned eight punts for 94 yards and four kickoffs for 85 yards.
Junior Tarean Folston is Notre Dame's leading returning rusher and finished the spring as the team's top running back. Bryant had split second-team carries with redshirt junior running back/receiver C.J. Prosise.
Notre Dame, No. 11 in the preseason Amway Coaches Poll, opens fall camp Friday in Culver, Indiana.