Classmates told local media outlet KTLA-5 that Diego had been previously bullied at school and on social media.
He was pronounced dead on Tuesday night (local time) "as a result of injuries sustained in the attack", the Riverside County Sheriff's Department said in a statement.
The two attackers, who were also both 13, have been charged with suspicion of assault likely to produce great bodily injury in connection with the attack and remained at Riverside County Juvenile Hall.
Officials have not said if charges against the teenagers would be increased since the victim's death.
Administrators at the California school have said that the two attackers had not shown any previous aggression and were good students.
Parents at the school are outraged at the bullying incident that led to Diego's death.
"This is a life-changing tragedy for everyone involved, including the staff and students at Landmark Middle School," Moreno Valley Mayor Yxstian Gutierrez said.
The family plans to donate Diego's organs "to transform this tragedy into the gift of life for other children", the sheriff's department said.