He was educated at Achimota School and proceeded to Kings College, Cambridge University in United Kingdom where he read Classics and graduated with First Class Honours in 1951. He joined the faculty of University of Ghana in 1953, received his Ph.D. in Classics in 1957 and became a full professor in 1962.
The Alexander Kwapong Hall at the University of Ghana was named after Professor Kwapong  at the University of Ghana.
He was once a chairman of Council of State He was awarded the 1981 Simba Prize for Scholarly Essays (Rome) and the author of many articles in scholarly journals. Professor Kwapong has served on numerous boards, including the Aspen Institute for Humanistic Studies and the International Council for Educational Development, the Association of African Universities, the Association of Commonwealth Universities(President, 1971), the International Association of Universities, and the International Council for Philosophy and Humanistic Studies (Vice-President) and was a chairman of the Education Review Committee of Ghana. Also has a house named after him in Achimota School 
- "Prof Alexander Kwapong passes away". www.graphic.com.gh. Daily Graphic. 2014-08-14. Archived from the original on 26 August 2014. Retrieved 22 August 2014.
- "Dr. Alex A. Kwapong". www.zoominfo.com. Zoom Info. Archived from the original on 26 August 2014. Retrieved 22 August 2014.
- "University of Ghana inaugurates hall in honour of first female graduate". www.vibeghana.com. Vibe Ghana. Archived from the original on 26 August 2014. Retrieved 22 August 2014.
- "Council Of State Chairman Violates Constitution". www.modernghana.com. Modern Ghana. 2002-09-04. Archived from the original on 1 December 2016. Retrieved 22 August 2014.
- "Professor Alexander A Kwapong". www.reconnectafrica.com. Reconnect Africa. Archived from the original on 26 August 2014. Retrieved 22 August 2014.
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