Galloway was the son of Frank and Louise Parler Galloway. He graduated from the Alabama School of Fine Arts. He attended the Memphis Academy of Art and earned a bachelor of fine art at the Atlanta College of Art. He remained in Atlanta for most of his career, where he was represented by the Marcia Wood Gallery.
In much of his later work, Galloway focused on intimate scenes from nature, often depicting reflections of the sky in water beneath forest trees. He generally painted in super-realistic detail with oils on sheets of oxidized metal.
Galloway's work was featured in several solo exhibitions at area galleries, including Amanda Schedler Fine Art in 2002, Schedler-Minchin Fine Art in 2005, Northport's Kentuck Art Center in 2007, and Clay Scot Gallery in 2010. His work is in the collections of the Southern Progress Corporation, Hartsfield Jackson Atlanta International Airport, Turner Entertainment Group, the Federal Reserve Bank of Atlanta, Comerica Bank, Royal Caribbean's Jewel of the Seas, and Mobile's Centre For The Living Arts.
Folsom, Hervey (July 2, 1999) "Fine Art grad's work is part of exhibit." Birmingham Post-Herald
- Gunter, Jennifer N. (May 2004) "Canvas: Drew Galloway." Birmingham magazine
- Jordan, Phillip (September 30, 2004) "A River Find Its Artists." Birmingham Weekly
- Feaster, Felicia (July 11, 2012) "Paintings beautifully capture light, water." Atlanta Journal-Constitution
- "Andrew Kirklyn Galloway." obituary (September 19, 2018) The Birmingham News
- Levine, Brett (October 4, 2018) "Remembering Artist Drew Galloway."
- Drew Galloway at Marcia Wood Gallery