The Salford taxi driver was delivering aid to Syria in December when he was kidnapped and then held hostage by IS.
IS threatened to kill him in footage last month showing the death of Briton David Haines, and in this video they threaten US aid worker Peter Kassig.
David Cameron said Britain would do all it could "to hunt down these murderers and bring them to justice".
The prime minister said the killing of father-of-two Mr Henning, 47, showed "how barbaric and repulsive" IS was.
"My thoughts and prayers tonight are with Alan`s wife Barbara, their children and all those who loved him," he said.
"Alan had gone to Syria to help get aid to people of all faiths in their hour of need."
Mr Henning`s wife Barbara had this week appealed for her husband`s release, saying: "He is innocent."
Volunteer Mr Henning was on his fourth aid mission to Syria when he was captured within minutes of arriving in the country last December.
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