Norris is a popular tourist and recreation destination, and in summer 2005 TVA opened a new visitor center at the dam. Visitors can learn about the history of Norris, hydropower operations, and TVA's management of the river system. The facility, located at the top of the dam, is open Monday through Saturday from 9 a.m. to 5 p.m. and Sunday from 1 to 5 p.m. It's staffed by TVA retiree volunteers.

In the 1930s, TVA established demonstration public parks at several locations on Norris Reservoir, including Cove Lake, Big Ridge, and the area around Norris Dam. These parks later became the nucleus of Tennessee's state park system.

Norris features three hiking trails. The River Bluff Trail is the longest at 3.1 miles and offers rich pockets of wildflowers. The Edge Path is a shady corridor with wheelchair access. The Songbird Trail is, as the name suggests, a popular area for birding.

Water sports at Norris include boating, water skiing, swimming, and excellent fishing. The Tennessee state record brown trout was caught in the waters of the Clinch River below Norris Dam.

The area around the Clinch River receives more than 45 inches of rain a year. In the past, floodwaters on the Clinch sometimes inundated areas hundreds of miles downstream. Norris Reservoir is an important component of the system TVA set up to reduce the risks of these disasters.