Harley-Davidson Inc. plans to shift more production overseas to avoid European Union tariffs on its iconic motorcycles, the latest manufacturer to reconfigure operations amid a widening global trade fight.

Harley prizes its made-in-the-USA reputation as central to its appeal to customers all over the world. But the Milwaukee company has opened factories in Brazil, India and Australia to tap international markets and hold down prices as sales falter in the U.S.

That...