Rawlings, a more than century-old company that produces the official ball and helmet of Major League Baseball, will be changing hands in a $395 million deal that adds the professional league as a key investor.

Under the terms of the deal announced Tuesday, consumer-goods conglomerate Newell Brands Inc. is selling the St. Louis sporting-goods maker to Seidler Equity Partners, a California-based private investment firm, and the MLB.

“This...