The town was named for General Oliver Wolcott, a signer of the Declaration of Independence.

The Lamoille River crosses the southern part of the town from east to west, followed by Vermont Route 15, which leads northwest 8 miles (13 km) to Morrisville and southeast 6 miles (10 km) to Hardwick.

The district is represented in the Vermont House by Daniel Noyes (D) and Kate Donnally (D).

The Fisher Covered Railroad Bridge is the easternmost access point for the Lamoille River Paddlers Trail in Wolcott.

Boaters can also access the Paddlers Trail three miles downstream at the Elmore (Pond) Road bridge to avoid a portage around the Wolcott Dam.