They say one of them set fire to items that led to the building burning down.
The fire broke out at the vacant Toomath's building on Ghuznee St in Wellington on 15 October, sending smoke billowing out around the central city.
The fire started at about 2:30pm and caused serious structural damage to the building.
Police earlier appealed for information about a group of youths seen leaving the area.
Detective Senior Sergeant Tim Leitch said police investigating the cause of the fire had now identified and located them.
Leitch said the four youths were from Wellington, had spoken with police and were understood to have been in the building at the time the fire started.
He said all four would be referred to youth services for unlawfully being in the building.
One of the young people has also been referred for setting fire to items, which caused the building fire.
The two-storey building, which was more than 100 years old, was designated as a quake-prone building about 20 years ago and had stood empty since 2019. Demolition work began this week.
