Drugabuse.gov defines addiction as “a chronic, relapsing brain disease that is characterized by compulsive drug seeking and use, despite harmful consequences. It is considered a brain disease because drugs change the brain; they change its structure and how it works.” I would add that alcohol would qualify in the use of the word drug in this definition.
In a controversial move in 1956, the American Medical Association (AMA) classified alcoholism as a disease. More recently, the American Society of Addiction Medicine (ASAM) further defined addiction as a disease after a thorough four-year process with input from over 80 experts including top addiction authorities, addiction medicine doctors, and eminent neuroscientists. More can be found here.
There are basically 5 criteria to classify something as a disease: It must be an illness that is primary (stands alone), chronic (lasts a long time), progressive (left untreated, it gets worse over time), causes morbidity (makes us sick), and is potentially fatal.