A new and distinct variety of peach tree, denominated ‘Rich Joy’, has firm, freestone, melting, yellow flesh fruit with normal acidity, rich flavor, good eating quality, and long shelf life on trees and after harvesting. The fruit typically ripen about one week after ‘Julyprince’ in mid-July in Byron, Ga., have a high percentage of red blush with an attractive yellow ground color on skin surface, and usually are almost round with a slightly prominent suture. The tree is moderately vigorous and semi-spreading in growth habit, has self-fertile showy pink flowers, and regularly bears heavy annual crops. This variety has a winter chilling requirement estimated at approximately 850 chill hours and is suited for high chill areas.