Consumer confidence hit an 18-year high in September, a positive indicator for spending going into the holiday shopping season, as robust job growth and a strong economic outlook bolstered Americans’ expectations for the future.

The Conference Board, a private research group, said Tuesday its index of consumer confidence rose to 138.4, up from 134.7 in August—the highest level since September 2000, which represented the late stages of the 1990s technology boom. An index reading of 100 represents how households saw the economy...