A video released early on Sunday purported to show David Haines being beheaded by Islamic State (I.S.) militants.
Mr Haines, 44, was seized in Syria in 2013 and was being held by Islamic State militants who had already killed two US journalists.
Justin Welby called on every church to pray for the aid worker who was born in England but raised in Scotland.
The archbishop told the BBC: "What we have seen in this dreadful video is an act of absolute evil, unqualified, without any light in it at all.
"There is a sense that within this area, and in many places in the world where this kind of thing is being done, that the darkness is deepening.
"It's being done in the name of faith, but we've heard already today faith leaders from Islam across the world condemning this.
"What's going on is a power-seeking activity. Faith is often used as a hook on which to hang other desires, and this is a desire for power and influence, and faith is being twisted to enable it to be used to gain power and influence for their own unspeakably evil ends.
"So today there is that sick sense of horror at the wickedness we see, a deep sense of compassion for the family, and prayer that they may be comforted by the presence and light of Christ in a very, very dark time indeed."
Prime Minister David Cameron said the UK would track down Mr Haines' killers but said current UK policy on dealing with I.S. would not change.
Mr Cameron said: "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 family spoke of the joy he felt when he learned he got his job in Syria. 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.
"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.
"They are killing and slaughtering thousands of people - Christians, Muslims, minorities across Iraq and Syria. They boast of their brutality. They claim to do this in the name of Islam. That is nonsense. Islam is a religion of peace. They are not Muslims, they are monsters."
A second British hostage, named as Alan Henning, was also shown in the video - with a threat that he would be the next to be killed.