Haines, a 44-year-old father of two from Perth, Scotland, was kidnapped last year while working for the French agency ACTED.
The video entitled, "A Message to the Allies of America," opened with UK Prime Minister David Cameron talking about working with the Iraqi government and allied Kurdish Peshmerga forces to defeat Islamic State.
"This British man has to pay the price for your promise, Cameron, to arm the Peshmerga against the Islamic State," said a masked man dressed in black with a British accent, standing over Haines, who was shown kneeling and wearing an orange jumpsuit.
The video then showed the beheading of the kneeling man.
At the end of the video, another hostage, identified as Alan Henning, was shown and the masked man said he would be killed if Cameron continued to support the fight against Islamic State.
Cameron condemned the killing and said he would bring the killers to justice.
"This is a despicable and appalling murder of an innocent aid worker. It is an act of pure evil. My heart goes out to the family of David Haines who have shown extraordinary courage and fortitude throughout this ordeal," he said in a statement released by Downing Street.
"We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes."
US President Barack Obama strongly condemned "the barbaric murder" of Haines and vowed to work with other countries to "destroy this threat to the people of our countries, the region and the world."
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve," Obama said in a statement. "We will work with the United Kingdom and a broad coalition of nations from the region and around the world to bring the perpetrators of this outrageous act to justice."    
In the video, Haines also spoke, saying Cameron was responsible for his execution. "You entered voluntarily into a coalition with the United States against the Islamic State, just as your predecessor, Tony Blair, did," he said.
"Following a trend amongst our British prime ministers who can't find the courage to say no to the Americans. Unfortunately, it is we, the British public, that will in the end pay the price for our Parliament's selfish decisions."
Foley and Sotloff made similar speeches to Obama, which have been dismissed as scripted by Islamic State and delivered under duress.
The purported executioner appeared to be the same man who appeared in videos with Foley and Sotloff, and it showed a similar desert setting. In both videos, the captives wore orange jumpsuits.
The United States resumed air strikes in Iraq in August for the first time since the withdrawal of the final U.S. troops from the country in 2011.
The raids followed major gains by Islamic State, which has declared an Islamic caliphate in areas it controls in Syria and Iraq.
Obama is calling for a coalition of Western and Middle Eastern countries to fight Islamic State and has said the United States intends to bomb Islamic State positions in Syria.
Britain has delivered humanitarian aid, carried out surveillance, given weapons to Kurds and promised training in Iraq. On military action, Britain supports US air strikes and Cameron has said repeatedly that Britain itself has ruled nothing out except combat troops on the ground.
Haines' family appealed earlier on Saturday to his captors to respond to their messages.
"We are the family of David Haines," relatives said in a statement released by Britain's Foreign Office.
"We have sent messages to you to which we have not received a reply. We are asking those holding David to make contact with us."
Paris-based ACTED previously said that Haines had been engaged in humanitarian work since 1999, helping victims of conflicts in the Balkans, Africa and the Middle East and that he was taken hostage in March 2013 in Syria.

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