Oakham was first settled in 1749 as part of Rutland, and was officially incorporated in 1762. It was originally named Oakhampton, but the name was changed for an unknown reason.

The village of Coldbrook Springs is part of Oakham, near the Barre line.

According to the United States Census Bureau, the town has a total area of 21.5 square miles (56 km²), of which 21.1 square miles (55 km²) is land and 0.4 square miles (1.0 km²), or 1.90%, is water.

Oakham is bordered by Barre to the northwest, Rutland to the northeast, Paxton to the southeast, Spencer to the south, and New Braintree to the southwest. The towns of Oakham, New Braintree, Spencer and North Brookfield share a common town corner; however, due to its location within feet of the banks of Brooks Pond, there is no direct way to get to North Brookfield from Oakham.

As of the census of 2000, there were 1,673 people, 578 households, and 467 families residing in the town. The population density was 79.2 people per square mile (30.6/km²). There were 591 housing units at an average density of 28.0 per square mile (10.8/km²). The racial makeup of the town was 98.33% White, 0.36% African American, 0.12% Native American, 0.60% Asian, 0.24% from other races, and 0.36% from two or more races. Hispanic or Latino of any race were 1.02% of the population.

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