Olejniczak was born on August 18, 1908 to John A. and Victoria Olejniczak in Green Bay, Wisconsin. He was a lifelong resident of the city and on November 24, 1938, married Regina Bettine at St. Francis Xavier Cathedral in Green Bay. Dom and Gina adopted two sons, Thomas Marshall Olejniczak and Mark Dominic Olejniczak.
Olejniczak served as alderman from 1936 to 1944 and as a mayor of Green Bay from 1945 to 1955. During his tenure as mayor, the city of Green Bay built a pipeline to Lake Michigan for its water supply and the beltline around the city was planned and developed.
Olejniczak's love for the Green Bay Packers began when the team was young. He was attending East High School and lived not far from the stadium, which at that time was located on East High School grounds. At that time, a youngster could walk into the stadium with a player and carry his headgear and Dominic was among them. His interest never waned. He continued to be an ardent backer during his years as alderman and as mayor. On July 10, 1950, Olejniczak was named to the Green Bay Packers Board of Directors and the bond grew stronger. In his dual role as mayor and board member that year, he was a leader in the civic drive that netted more than $100,000 and helped save the franchise.
Olejniczak was named to the Executive Committee of the Green Bay Packers Board of Directors in January 1952. Six years later, in 1958, he became President of the franchise. When he took over the Packer presidency, the team had not had a winning record in 10 years. Olejniczak was a prime mover in building the new City Stadium and was instrumental in hiring New York Giants assistant Vince Lombardi in 1959.
After serving 24 years as Packers president, more than anyone in the team's history, Olejniczak resigned on June 1, 1982, and was succeeded by Robert J. Parins. At that time, Olejniczak was named the first Packer Chairman of the Board and served in that role until 1989. He was inducted into the Green Bay Packer Hall of Fame in 1979.
Prior to entering public service, Olejniczak was a real estate broker. He received the Knighthood of St. Gregory from Bishop Wycislo and an honorary Doctorate of Law Degree from St. Norbert College in 1986. He was the first lay President of Premontre High School (later Notre Dame de la Baie Academy).