The wording of the orders – which come into effect in 45 days – is vague but leaves open the possibility that hosting the apps in the Apple and Google app stores could be covered by the ban.
Mr Trump had threatened a deadline of September 15 to “close down” TikTok unless Microsoft or “somebody else” bought it.
TikTok, Microsoft and WeChat owner Tencent did not immediately respond to requests for comment.
TikTok is a video-sharing app that is widely popular among young people.
It is owned by the Chinese company ByteDance, which operates a separate version for the Chinese market.
TikTok insists it does not store US user information in China and would not share it with the Chinese government.
WeChat and its sister app Weixin in China are hugely popular messaging apps, with many Chinese expatriates using WeChat to stay in touch with friends and family back home.
The apps are owned by Tencent, a major Chinese digital conglomerate.
WeChat also says it does not share data with the Chinese government and never has, and does not store international user data in China.