His lawyers said Vickers was already serving a “life sentence” after Scarlett’s death.
Jurors spent 13 hours and 21 minutes deliberating their verdict before reaching a majority agreement, with 10 finding Vickers guilty of murder.
He was remanded in custody to be sentenced on 10 February.
Det Supt Craig Rudd of Durham Police said Scarlett had had “her whole life ahead of her” but it was “cruelly cut short by a man who was meant to protect her”.
He added: “We may never know why or what caused Simon Vickers to do what he did that night.
“Sadly, today’s verdict will not bring Scarlett back, but he will now face the consequences of his actions.”
