Yeun was born in Seoul on December 21, 1983, to Je and June Yeun. His father was an architect in South Korea before moving his family in 1988 to Canada, where they lived in Regina, Saskatchewan. In Regina, he attended Ruth M. Buck Elementary School. He has a younger brother named Brian. The family later moved to the U.S. and settled in Taylor, Michigan, and then Troy, Michigan, where Yeun lived until he graduated from Troy High School in 2001. Growing up, Yeun's family spoke Korean at home.
Yeun was raised in a Christian household. His parents, who owned beauty-supply stores in Detroit, began calling him "Steven" after meeting a doctor by that name. He received a bachelor's degree in psychology with a concentration in neuroscience from Kalamazoo College in 2005. At Kalamazoo, he befriended the sister of comedian Jordan Klepper and she took him to see Klepper's improv show, which inspired him to take his first acting class and later follow Klepper to Chicago, where they joined The Second City.
