Celina was founded in 1834 in a swampy, wooded area that had to be drained and cleared before it could be settled. What remained was a level town surrounded by rich farm fields.

When one of the town's founding fathers was traveling through New York state to get the town platte lithographed, he came across the town of Salina situated on the edge of Onondaga Lake near Syracuse. Noting the similarity between Salina and the newly founded settlement in Ohio, he named the new town Celina.