Joseph Dominelli was born in Schenectady, New York, on August 11, 1917. Son of Joseph and Madeline Campachero Dominelli, he attended Mount Pleasant High School and, in 1939, married his wife, Florence. In 1943, Dominelli was drafted into the U.S. Army and on June 6, 1944, he went ashore on Omaha Beach in Normandy, France. After being wounded and being returned to his unit, Dominelli received his most serious wounds in Germany later that year. In 1945, he was honorably discharged at the Thomas M. England General Hospital and returned home with three purple hearts and three bronze stars.

In 1947, Dominelli joined the Rotterdam, New York, Police Department, becoming the seventh police officer at the agency. He immediately became involved in the Police Benevolent Association (PBA) and the Police Conference of New York (PCNY). Eventually, he was elected as president of the Rotterdam PBA and vice president of the PCNY.