The popular app, which is used by more than 170 million American users, went dark briefly last month in the US as the ban deadline approached.
Trump then signed an executive order granting TikTok a 75-day extension to comply with a law banning the app if it is not sold.
According to Bloomberg, which first reported TikTok's return to app stores in the US, the decision to resume its availability came after Apple and Google received assurances from the Trump administration that they would not be held liable for allowing downloads, and the ban wouldn't be enforced yet.
The ban, which passed with a bipartisan vote in Congress, was signed into law by former President Joe Biden. It ordered TikTok's Chinese owner ByteDance to sell the US version of the platform to a neutral party to avert an outright ban.
The Biden administration had argued that TikTok could be used by China as a tool for spying and political manipulation.
China and TikTok have repeatedly denied those accusations. Beijing has also previously rejected calls for a sale of TikTok's US operations.
The law banning the app was supported by US lawmakers on both sides of the aisle and it was ultimately upheld by the Supreme Court.
Trump himself had supported banning the app during his first term in office but he appeared to have a change of heart last year during the presidential race.
He professed a "warm spot" for the app, touting the billions of views he says his videos attracted on the platform during last year's presidential campaign.
