WASHINGTON—The U.S. military campaign against Islamist militants in Syria is being designed to allow President Barack Obama to exert a high degree of personal control, going so far as to require that the military obtain presidential signoff for strikes in Syrian territory, officials said.

The requirements for strikes in Syria against the extremist group Islamic State will be far more stringent than those targeting it in Iraq, at least at first. U.S. officials say it is an attempt to limit the threat the U.S. could be dragged...