Israel Hernandez-Llach, 18, was confronted by officers when they found him spray-painting an abandoned fast food building on Tuesday morning.
He fled the scene, leading officers on a foot chase through Miami Beach, before he was cornered and shot with the Taser when he ignored orders to stop.
Miami Police Chief Ray Martinez said: “The officers were forced to use the Taser to avoid a physical incident.”
Mr Hernandez-Llach, a talented artist, was shot once in the chest and collapsed.
Chief Martinez said officers noticed he was in distress and the teenager was taken to Mount Sinai Hospital, where he was later pronounced dead.
The death is under investigation by the city and the state attorney’s office.
Chief Martinez added: “The city of Miami Beach would like to extend their condolences to the family of Israel Hernandez.”
The teenager’s sister, 21-year-old Offir Hernandez, said the family wanted answers.
She added: “He wanted to change the world somehow through art.”
Their lawyer, Tod McPharlin, has called for an independent investigation