The 62 year-old bronze statue by sculptor Walker Hancock was stolen from in front of Wilner Auditorium in 1987.
Other stolen artworks have been returned over the years, but the Frost statue was the only unrecovered piece of stolen art from the museum.
"We're thrilled that it's been returned because it belongs here at Wichita State," said museum spokeswoman Teresa Veazey.
Wichita State Police received a tip recently about the possible location of the statue and contacted authorities in Missouri who found and recovered it.
"It was recovered in the garage. It was collecting dust," said WSU Police Detective Jeff Rider. Rider is confident the man who took it has been in possession of the bust the entire time.
The 44-year-old man was arrested and facing charges receiving stolen property, police said.
It's unlikely he would face any charges in Wichita because the statute of limitations has long expired.
Veazey said the art piece looks to be in good condition. The museum plans to put it back on display outside in a few months.