Joshua Kelley was born and raised in Lancaster, California which is just north of where he wound up playing football professionally. He attended Eastside High School where he starred as both a running back and kick returner. His senior season, Kelley rushed for 1,469 yards and 16 touchdowns on top of catching 19 passes for another 352 yards and six more scores. That performance earned him Golden League Back of the Year honors and a selection to the All-Golden League First Team.
Out of high school, Kelley committed to play for UC Davis. During his two seasons there, he rushed for a combined 1,139 yards and seven touchdowns.