The power President Trump is lawfully exercising in the executive order to control the Executive Office of the President of the United States stems from the Reorganization Act of 1939 (via https://en.wikisource.org/wiki/Executive_Order_8248) which FDR had to get Congress to pass after his previous efforts to reorganize the executive branch during the Great Depression were deemed unconsititutional.

Critics at the time warned this Act would give the president too much power.