Archbishop Justin Welby wrote a letter on the man's behalf ahead of an appeal against his second rejected asylum claim, to support his case.
The man has already had his asylum case rejected twice and is appealing for the right to make a third attempt.
In the meantime, the asylum seeker must report to a Home Office centre every two weeks or will be held in a detention centre.
The Archbishop's interfaith adviser, Mark Poulson, also wrote a letter to "unequivocally endorse" an appeal for asylum. Poulson and Dr Welby met the man while he was working as a volunteer.
Dr Welby wrote in his letter that he had "been impressed with his positive attitude, integrity and quality of his work".
"[The man] is clearly someone who wishes to contribute to society ... He is someone who would be a great asset to the United Kingdom. I strongly endorse [his] desire to seek asylum in the UK," the letter continued.
The Guardian reported that the man, a Syriac Orthodox Christian, fled Mosul in August 2014 with his family after the Nineveh Plains genocide.
Between 100,000-200,000 Christians and religious minorities fled after IS fighters threatened to kill any non-Sunnis who remained in the area.
Both judges who have examined the man's case say that the man will be able to join his family in the Irbil - an area of Iraqi Kurdistan - who the judges claim "appear to live in safety".
The man's solicitor, Susan Liew, told the Guardian that the ruling is "irrational" because his family in Irbil live in a church basement because they have nowhere else to go.
The man said: "I feel safe in Britain. I can't go back to Kurdistan, it's a different government, it's not our country. They don't deal with us like people from the same place. It's a different language."
Archbishop Welby has repeatedly supported Iraqi Christians, and has urged the government to do more to help those who were expelled by IS.