WASHINGTON—President Trump signed an executive order on Tuesday that seeks to give his political appointees far-reaching control over federal agencies that for decades have operated independently of White House influence.

A regulatory expert said the directive will likely be challenged in court, as Congress has largely shielded some of the affected agencies from involvement by the White House.

The executive order would affect agencies like the SEC and FDIC, but it excludes the Federal Reserve's Board of Governors and Open Market Committee.