Spence played for Ohio State in 2012 and 2013 before being suspended and eventually declared ineligible after failing two drug tests. He was initially suspended for the 2014 Orange Bowl and the first two games of the 2014 season after testing positive for ecstasy last December.
A second positive test late this summer caused the Big Ten to indefinitely suspend Spence and eventually deny his appeal for reinstatement in November.
Spence's father, Greg, said Noah considered several FCS transfer destinations but settled on Eastern Kentucky.
"It's a great institution that has a wonderful family atmosphere, which he was used to from being at Ohio State," Greg Spence said. "Coach [Dean] Hood and his coaching staff are wonderful gentlemen that take care of the student-athlete as a whole person, on the field and off. Something Noah really needed as a continuum from what Coach [Urban] Meyer has been doing.
"He's extremely excited to play football again as well as grateful for another opportunity."
SI.com earlier reported Spence's transfer decision.
Noah Spence, a former five-star recruit, recorded eight sacks and 14.5 tackles for loss in 2013, earning first-team All-Big Ten honors. He explored entering the NFL draft and had been projected as a third- to fifth-round draft pick. But he opted for another year in college. Noah is on track to graduate in December.
"Noah needed another year of growth and maturity, especially regarding decision-making," Greg Spence said, "so he could have a long, sustained career at the next level."
Greg Spence said his son has sought help with his past issues.
"He continues to be open and receptive to all of the guidance that has been provided professionally and non-professionally in regards to those areas of concern," Greg Spence said.
Greg Spence thanked Meyer and the Ohio State coaches for their support and for keeping Noah involved with the team during its run to a national championship.
"They continue to stay in his corner," Greg Spence said.