In 1998, Glover received the Flagstar Award by ACRAG (the Arts Critics and Reviewers Association of Ghana), and was also honoured with the distinguished alumni award from the African-American Institute in New York City. He has received several national and international awards, including the Order of the Volta in Ghana in 2007, the Millennium Excellence Award in 2010 and is a Life Fellow of the Royal Society of Arts, London. He is also a Fellow of the Ghana Academy of Arts and Sciences.