The family of Trevor Smith say the body found near the Waikato River is his.

It was discovered near the river's edge yesterday, three weeks after he wandered off while visiting a sick relative at Waikato Hospital.

Trevor Smith had mild dementia and his brother Steve Smith says it appears the 70-year-old fell about four metres down a steep bank.

Steve Smith says he's grateful to all the people who helped in the search for his brother.

Police are yet to complete the formal identification process.