GDPR, the European Union’s new privacy law, is drawing advertising money toward Google’s online-ad services and away from competitors that are straining to show they’re complying with the sweeping regulation.

The reason: the Alphabet Inc. ad giant is gathering individuals’ consent for targeted advertising at far higher rates than many competing online-ad services, early data show. That means the new law, the General Data Protection Regulation, is reinforcing—at least initially—the strength of the biggest online-ad players,...