General Electric Co. will drop out of the Dow Jones Industrial Average next week, a milestone in the decline of a firm that once ranked among the mightiest of blue-chips and was a pillar of the U.S. economy.

It will be replaced by drugstore retailer Walgreens Boots Alliance Inc., the latest sign of the rise of the global consumer economy and the postcrisis boom in debt issuance that has fueled a worldwide deal-making frenzy.

The...