Demetrius Hewlin died hours after Russell King Jr., 17, was declared brain dead. Daniel Parmertor, 16, died shortly after Monday’s shooting.
Gunfire broke out at Chardon High School at 07:30 a.m. on Monday.
The suspected shooter, who has been identified by Geauga County Juvenile Court as TJ Lane, appeared in court on Tuesday for a preliminary hearing.
Two other victims remain in hospital, with one said to be in a serious condition and the other stable.
A vigil will take place in the community on Tuesday night, and schools will stay closed until Friday.
Prosecuting lawyer David Joyce said TJ Lane admitted to firing 10 shots from a .22 calibre handgun at a group of students.
“He did not know the students but chose them randomly,” David Joyce told the court.
Judge Timothy Grendell ordered that TJ Lane be held in a juvenile detention facility for up to 15 days. Prosecutors have until 1 March to bring charges against him.
The judge also imposed a gag order on lawyers from both sides, and has prohibited the media from showing images of the suspect’s face, as he is a minor.
Demetrius Hewlin, who died on Tuesday, had been in critical condition in hospital after the shooting took place.
His family described him as a “happy young man who loved life, his family and his friends”.
“We will miss him very much but we are proud that he will be able to help others through organ donation,” they said in a statement.
Early on Tuesday morning Russell King Jr., 17, was declared brain dead, although he still has a heartbeat, the Cuyahoga County medical examiner’s office said.
That announcement followed news that the first victim had died on Monday. Daniel Parmertor, 16, was declared dead after being taken to hospital immediately after the shooting.
Daniel Parmertor had been waiting in the cafeteria for a bus to a vocational school.
“We are shocked by this senseless tragedy,” his family said in a statement.
“Danny was a bright young boy who had a bright future ahead of him.”
A student who witnessed the attack told US media it appeared that the gunman targeted a group of students sitting together.
Local news reports said the suspect was chased out of the building by a teacher before turning himself in to two people in the vicinity of the school.
“I am happy to tell you that the student that did the shooting is captured,” a sheriff’s official said to reporters at the scene.
“He actually turned himself in to a couple of innocent bystanders just north of the city here in Chardon township.”
Chardon High School has about 1,100 pupils, and the town itself – about 30 miles (48 km) east of the city of Cleveland – is home to about 5,000 residents.
US high schools and university campuses are no stranger to gun attacks, and many have well-drilled security and emergency response procedures in place aiming to prevent attacks and manage the response if a gunman does attack.
Monday’s shooting was the worst incidence of gun violence at a US high school in 11 months and the worst shooting in Ohio since late 2007, the Brady Center to Prevent Gun Violence told Reuters news agency.
In the most notorious shooting, two students at Columbine High School in Colorado killed 12 students and a teacher in April 1999.
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