Two other students were injured, one seriously, said university president Jim Ryan.
Local police chief Timothy Longo added that the suspect, 22-year-old college student Christopher Darnell Jones Jr, had been arrested and charged with murder.
He was arrested in a suburb of Richmond, about 100 miles from the main campus of the University of Virginia (UVA) in Charlottesville, according to Henrico County police.
A UVA team tasked with investigating students who may pose a security threat had previously been seized of Mr Jones Jr, after a report that he had a gun, but no weapon had been found, said clarified Timothy Longo.
The shooting took place aboard a bus when the students were returning from an excursion where they had attended a play, said President Jim Ryan.
The campus, sealed off overnight and crisscrossed by patrols and helicopters looking for the suspect before his arrest, has now reopened, Ryan said. Classes for the day have been cancelled.
The White House on Monday expressed its condolences to the families of the victims, condemning “a senseless shooting” and calling on Congress to toughen laws on small arms.
“Too many families across America must bear the terrible burden of gun violence,” executive spokeswoman Karine Jean-Pierre wrote in a statement. “We must ban assault rifles to remove these weapons of war from American streets,” she continued.
“It’s a day of incredible sadness,” said Tim Ryan. “The whole university is in mourning this morning.”
He called on those who “needed help” to call on the resources deployed by the university, including psychological support.
Virginia Governor Glenn Youngkin, citing on Twitter a “horrifying tragedy” where families’ lives were “transformed forever”, praised the work of law enforcement that led to the arrest.
School shootings are common in the United States, and each time revive the debate on better supervision of firearms.
In April 2007, such a tragedy had already struck Virginia: an unbalanced student had shot dead 32 people on the campus of Virginia Tech University, in Blacksburg, before committing suicide.
Virginia Democratic Senator Tim Kaine tweeted Monday that he was “deeply moved to learn that more Virginians have been wiped out by gun violence.”
Drama in Idaho
The emotion caused by this tragedy was further amplified by the announcement of the discovery on Sunday of the lifeless bodies of four students from another establishment, the University of Idaho (north-west).
“It is with great sadness that I share with you information notified to the university today of the deaths of four University of Idaho students who lived off campus and were allegedly victims of ‘Homicide,’ said facility president Scott Green in a statement.
Police in the city of Moscow, where the bodies were found, have opened an investigation.
The police, however, consider that the situation does not present a “direct threat”, added Mr. Green.
A third incident added to tensions Monday morning, when Oakland University, near Detroit, Michigan (north), asked its students and staff not to go to its campus, where police were looking for two armed suspects , before indicating a few hours later that everything was back to normal.