By Jeremy Cooke
BBC correspondent in Little Egg Harbor, New Jersey
This is a community in grief.
Ribbons, signs and vigils mark the death of one of the town's sons
All around Little Egg Harbor there are yellow ribbons and signs which read: "Our thoughts and prayers are with the Johnson family."
There have been prayer meetings and candlelit vigils but now all hope has been extinguished.
Paul Johnson left this community years ago. But many of his neighbours remember the engineer, and many more know his family, including his sister, who still lives here.
The family was expecting bad news. Once it was established that al-Qaeda had seized Mr Johnson there was little cause for optimism.
'Not the Saudi Paul knew'
Still, confirmation of his death has come as a bitter blow.
The family has not appeared in public, but they asked an FBI agent to read a statement.
Special agent Joseph Billy told reporters: "They... know that this act was done by extremists and does not represent the Saudi Arabia that Paul often spoke and wrote about...
"They understand the Saudis and the Americans did all they could under difficult circumstances."
Among shoppers at the local supermarket, there was a sense of shock, outrage and fear.
One man said: "It's devastating. I just don't know what I would do if it was my dad."
A woman added: "It's horrible. We live so close to his family. It's really scary."
Earlier this week, Mr Johnson's son, also called Paul, had made a direct televised plea for his father's kidnappers to set him free in time for Father's Day, which Americans celebrate this weekend.
The family had hoped to be welcoming Mr Johnson home.
Instead they are planning his funeral.