In a post on Facebook, Archbishop Welby wrote: "My thoughts and prayers are with the family of Ian Squire, the British man who we learned today was killed while being held hostage in Nigeria.
"Ian, an optician, was in Nigeria providing free vital medical aid to people. We pray for his family and friends as they come to terms with his death, and for the three other hostages who will have to deal with the mental and physical scars they suffered while in captivity.
"We pray for the areas in the Niger Delta area of Nigeria where there are high levels of crime and tension – for peace, restoration and reconciliation and God's kingdom to come in those communities and across all of Africa."
Yesterday, the Nigerian authorities said they had arrested four people in connection with the hostage-taking and killing.
The three other hostages, Alanna Carson, David Donovan and Shirley Donovan have returned home safely to the UK.
In a statement, the family said: "Alanna, Ian, David and Shirley were kidnapped in Nigeria some three weeks ago.
"We are grateful for the support received by the British High Commission, and help from the Nigerian authorities in negotiating their release. We are delighted and relieved that Alanna, David and Shirley have returned home safely. Our thoughts are now with the family and friends of Ian as we come to terms with his sad death.
"This has been a traumatic time for our loved ones who were kidnapped and for their families and friends here in the UK. We would therefore ask that the media respect our privacy as we come to terms with the news. We will not be making any further comment."