Agu, a junior from Bakersfield, Calif., was taking part in a conditioning run Friday morning when he collapsed. He was pronounced dead at a local hospital.
He appeared in seven games last season as a backup on the defensive line.
"This is a very difficult time for our football family," Dykes said. "Ted was a remarkable young man and a member of this family who was highly respected and loved by his teammates and coaching staff. He had an incredible passion for life and will be deeply missed."
A release from the Cal Athletic Department said the school was providing counseling for players.
"Our heartfelt condolences go out to Ted's family," Cal Athletics Director Sandy Barbour said. "This is a very painful time for the entire Cal family. In the days and weeks ahead, my focus will be on providing every member of our community the support and information they need to get through this time."