The 62 year old has led his diocese, which covers Belfast and other parts of Northern Ireland, for the past twelve years - a job which he said was an "amazing privilege and joy".
After being diagnosed with prostate cancer in 2018, Bishop Alan took a sabbatical while he underwent treatment.
He also took part in a clinical trial which he hopes will help others in future.
Speaking about his decision to step down, he said: "The last 12 months have been exhausting and it has been difficult to focus on anything other than my treatment plan. I have just received my last proton injection as part of the clinical trial and this stage of the journey is complete. I now need time to recover and regain my strength and energy.
"Having advanced prostate cancer means that I will be receiving quarterly hormone injections for the rest of my life and will have very regular check-ups with my oncologist. There are no guarantees, but it is hoped that I will be free of further treatment for years to come."
Bishop Alan will retire on 31st December this year and is expected to serve over the Christmas period.
Paying tribute, Archbishop of Armagh and Primate of All-Ireland, Most Rev Dr Richard Clarke, said: "With our prayers, we all wish for Bishop Alan a happy and fulfilling retirement.
"We know that the decision to retire on grounds of ill-health has been a difficult and painful one for him.
"For well over a decade, Alan has given powerful, courageous and dedicated service to the Diocese of Connor and to the wider Church of Ireland, and now to relinquish office in circumstances of ill-health is inevitably far from easy for him.
"We thank him warmly for all that he has given us and we wish him, Liz and their family every happiness and God's blessing into the future."
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