Goyke was born in Oshkosh, Wisconsin. He attended the University of Minnesota and graduated from Saint Mary's University. Goyke worked as a staff member for U.S. Senator and Vice President Hubert Humphrey.
Goyke was elected to the Senate in 1974 and was re-elected in 1978. In 1979, he was a candidate for the United States House of Representatives from Wisconsin's 6th congressional district in a special election following the death of William A. Steiger. He lost to Tom Petri. The following year, he ran again and lost again to Petri. Goyke remained in the Wisconsin Senate until 1983. During his time in office, Goyke served as the chair of several committees and subcommittees, including Education and State Institutions and Banking and Insurance.
Goyke is a member of the Fourth Degree of the Knights of Columbus. Additionally, he is a member of the Benevolent and Protective Order of Elks, the Fraternal Order of Eagles, the League of Women Voters, the Sierra Club and the Young Men's Christian Association. He is married with two sons. In November 2012, one of his sons, Evan Goyke, was elected to the Wisconsin State Assembly.
- "Goyke Gary R. 1947". Wisconsin Historical Society. Archived from the original on 2012-11-11. Retrieved 2011-12-14.
- "Gary Goyke". Clean Wisconsin. 2014-05-27. Retrieved 2019-01-27.
- Journal, PAT SIMMS For the State. "Executive Q&A: Politics the thread in a long career". madison.com. Retrieved 2019-01-27.