Murdered British hostage David Cawthorne Haines was a "British hero" who died in an "act of pure evil", said David Cameron.
Mr Haines' family spoke of their devastation over his death and warned Isil and radicalisation was a threat "to the wholesale safety of every person in the world".
In an emotional statement, his brother, Mike, said society as a whole had to deal with the problem and backed calls for returning jihadists to "face the consequences of their actions".
World leaders led tributes to the 44-year-old father-of-two after the terror group Isil carried out its threat to execute him in cold blood.
US President Barack Obama condemned the "barbaric murder" and vowed to help bring his killer to justice, while the Archbishop of Canterbury said he had been "evilly killed".
Mr Haines was apparently executed by a hooded Isil terrorist who appeared to be the same suspected Briton, known as "Jihadi John", who murdered two American journalists.
The aid worker, a former RAF engineer, was working for a French aid agency at the Atmeh refugee camp in northern Syria when he was abducted in March last year.
A second British hostage, named as Alan Henning, was also shown - with a threat that he would be the next to be killed.
Mr Cameron said: "David Haines was a British hero. The fact that an aid worker was taken, held and brutally murdered at the hands of Isil sums up what this organisation stands for." He added: "We will hunt down those responsible and bring them to justice no matter how long it takes.
"David Haines was an aid worker. He went into harm's way, not to harm people but to help his fellow human beings in the hour of their direst need, from the Balkans to the Middle East.
"His selflessness, his decency, his burning desire to help others has today cost him his life. But the whole country, like his grieving family, can be incredibly proud of what he did and what he stood for in his humanitarian mission."
Mr Obama said: "The United States strongly condemns the barbaric murder of UK citizen David Haines by the terrorist group Isil.
"Our hearts go out to the family of Mr Haines and to the people of the United Kingdom. The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve."
In a statement on behalf of the family, Mike Haines said his brother was "just another bloke" who would help anyone in need. He said: "Radicalisation remains the biggest threat to the wholesale safety of every person in the world."
Mr Haines's ex-wife Louise, 43, and his daughter Bethany, 17, were said to be "in shock" at their home in Scone, outside Perth, following his murder.
Mr Haines also has a four-year-old daughter by his second wife Dragana, who is Croatian. When captured he was in Syria working with the French aid agency, Acted.
A spokesman said: "The horrible assassination of David, an aid worker, goes against all humanitarian principles and is a crime against humanity."(© Daily Telegraph, London)
An 'Irish jihadi' fighting with ISIS has publicly defended the execution of David Haines, writes Tom Worden.
The fanatical convert - believed to be in his early 20s - claimed Mr Haines' former role in the RAF justified his killing.
The extremist, who was fighting in Syria, wrote: "David Haines was in the RAF for 10 years, the same RAF that bombs Muslims and gets involved in wars in the Muslim lands that has no direct threat and has nothing to do with Britain.
"Have you seen the track record of USA and UK how many innocent Muslims they have imprisoned and killed?"
The jihadist was writing today on the social media website Ask.fm. His account has since been suspended.
Using the name Muthenna ibn Abu on Ask.fm, he was asked "What did British aid worker David Haines do to your pathetic murdering army?" He replied, calling the UK government "hypocritical".
Muthenna, who describes himself as "half-Irish half-Nigerian" has previously described his life under ISIS - posing with AK-47 rifle.
He has encouraged Muslims as young as 16 to travel to Syria and Iraq to join the fanatical group.