WASHINGTON—President Biden revoked executive orders targeting the Chinese-owned TikTok and WeChat apps initiated by former President Donald Trump and signed a new order requiring security reviews of these and other apps in the jurisdiction of foreign adversaries.

The new executive order is designed to replace the Trump administration’s approach targeting individual companies with a broader process for reviewing risks posed by apps that are connected to potentially hostile countries, according to senior Biden administration officials.

The officials say they remain concerned about security risks from Chinese and certain other foreign-owned apps but that the executive orders signed by Mr.