The German teenager from Berlin named Admarsu Birhan by police was staying with Andy and Ruth Ive at their home in Burton in Lonsdale, close to the accident site, for the summer as part of an exchange scheme between organic farms and schools.
Mr Ive wrote on Facebook: "The helicopter crash near Burton in Lonsdale village has taken the lives of the pilot and the young German lad that has been living with us. There are no words."
The pilot has been named by police as Ian Macdonald, 66, who owned the helicopter and flew it regularly to and from his home in Burton in Lonsdale.
The aircraft was returning from Barrow-in-Furness in Cumbria, though the purpose of the flight is not known.
Mr Macdonald's partner Julia Smith's mother Audrey Smith posted: "With great sadness my daughter Julia’s partner Ian has been killed in a helicopter accident on Monday June 20 - love from all of us."
The village's parish council chair, Peter Thompson, told the Craven Herald that the community was 'shocked' after learning the identities of the two victims.
He added that Mr Macdonald was a 'great support' to the village and had worked with the local shop, which is run by volunteers.
The Air Accident Investigation Branch has opened an investigation into the crash at midday on June 20 and a team of inspectors were travelling to the accident site.
The light helicopter came down in a field near the village.