The body of John Shaffer, 42, of Charleston, S.C., was recovered Saturday afternoon, WLOS reported.
On Saturday morning, Shaffer jumped into the water to rescue his dog and was carried over the falls.
The dog has not been recovered yet.
Gorges State Park was closed during the recovery but has reopened.
Lake Toxaway Fire and Rescue Chief Carmon West said this is the first incident at Rainbow Falls since 24-year-old Georgia news anchor Taylor Terrell was swept over the falls in 2016.
U.S. Forest officials say the best way to enjoy a waterfall is at a safe distance. Authorities also advise to never play in the water above a waterfall because rocks can be slippery and it can be easy to lose balance with bare feet.