Floyd, 47, was found dead after police stormed the James T. Vaughn Correctional Center early Thursday morning, nearly 20 hours after a hostage situation began.
A large police motorcycle escort led the procession, while law enforcement officers, paramedics and firefighters saluted their fallen comrade.
RAW VIDEO: Procession for body of Sgt. Floyd
Also Thursday, Gov. John Carney ordered flags to be flown at half-staff, and he thanked the employees of the department of corrections.
"These brave men and women go to work every day knowing they may not come home, as do their families. We owe them an incredible debt of gratitude," Carney said.
Officers continued to stand together to show support as a flag-draped gurney was wheeled inside, and Sgt. Floyd's family is left grieving.
Kevin Chase says he recently spent a year and a half at another correctional center. He is shocked by what happened inside the facility in Smyrna
"I can't imagine that happening, can't fathom it," Chase said. I wish the guys would have went about it in a better way."
The medical examiner will work to determine the cause of Floyd's death.