According to Associated Press, the Sinai Province militants (formerly known as Ansar Beit al-Maqdis) admitted killing the man on its official Twitter account on Sunday.
"It published pictures of his passport and two identification cards," the newswire reported.
"It did not say when or how it killed him.
"The passport said he was a 58-year-old from Texas and his identification cards said he worked for Texas-based energy company Apache Corp and Qarun Petroleum Co, a joint venture with Egypt."
In August Apache revealed one of its supervisors died from a carjacking incident in Egypt but it did not identify the victim.
Security sources told Reuters that the victim's body was discovered in a car in the Western Desert region almost four months ago.
Apache spokeswoman Castlen Kennedy told the newswire that the US government was still investigating the incident.
"Out of respect for the family and the ongoing nature of the investigation, I cannot comment further," she reportedly said.
The Sinai Province militant group reportedly changed its name after pledging loyalty to the Islamic State this month.
"The group has become a major security problem for the government, killing scores of police and soldiers in the lawless Sinai Peninsula, which is bounded by Israel, Gaza and the Suez Canal, one of the world's most important shipping routes," the newswire reported.
"Last month, at least 33 security personnel were killed in two successive attacks, prompting Egypt to declare a three-month state of emergency in parts of northern Sinai and raze hundreds of homes to create a security buffer on its border with Gaza.
"If genuine, the group's killing of 58-year-old Henderson could mark a shift from its previous focus on targeting Egyptian police and soldiers and their local informers."