Blacksburg police on Monday identified the victim as David Campbell Gayle of Norfolk.
Michael Smith, also 19 and a sophomore at Virginia Tech, said he was visiting a friend at the same apartment building when he heard people run downstairs.
"We walked around back to make sure everything was OK. I tapped him on the shoulder but got no response," Smith said.
Emergency medical services arrived a short time later.
Witnesses say the student was trying to get on to the roof of the building when he fell.
Police say there was no damage on the balcony and that an autopsy will be performed on Monday.