Varney earned his medical degree (1988) and completed his residency in general internal medicine (1992) at SIU. He earned his bachelor's degree in pre-medicine and psychology at Augustana College (1983).
He received the Award for Excellence in Clinical Practice (1990) and the Barry Breen Memorial Award for Outstanding Resident (1988) during his residency in the SiU medicine department. He is board eligible in internal medicine.
A native of Ottawa, Varney and his wife, Carol, who is a certified speech pathologist at St. John's Hospital in Springfield, are the parents of two sons, Jacob and Nicholas. Varney is the son of Mr. and Mrs. Joseph Varney of Ottawa.