Like both legislative statutes and the regulations promulgated by government agencies, executive orders are subject to judicial review and may be overturned if the orders lack support by statute or the Constitution. Some policy initiatives require approval by the legislative branch, but executive orders have significant influence over the internal affairs of government, deciding how and to what degree legislation will be enforced, dealing with emergencies, waging wars, and in general fine-tuning policy choices in the implementation of broad statutes.

Basis in the United States Constitution

The United States Constitution does not have a provision that explicitly permits the use of executive orders. Article II, Section 1, Clause 1 of the Constitution simply states: “The executive Power shall be vested in a President of the United States of America.” Sections 2 and 3 describe the various powers and duties of the president, including “He shall take care that the Laws be faithfully executed”.

The U.S. Supreme Court has held that all executive orders from the president of the United States must be supported by the Constitution, whether from a clause granting specific power, or by Congress delegating such to the executive branch. Specifically, such orders must be rooted in Article II of the US Constitution or enacted by the Congress in statutes. Attempts to block such orders have been successful at times, when such orders either exceeded the authority of the president or could be better handled through legislation.

So yeah there is a legal basis

The problem arises when the person giving those orders authority hears “By order of the king” instead of “by directive of the president”.

The US doesn’t want a king, it was a big deal here about 250 years ago. Looking like it’s gonna be a big reminder for the 250 anniversary.

In the United States, an executive order is a directive by the president of the United States that manages operations of the federal government. […] Like both legislative statutes and the regulations promulgated by government agencies, executive orders are subject to judicial review and may be overturned if the orders lack support by statute or the Constitution. Some policy initiatives require approval by the legislative branch, but executive orders have significant influence over the internal affairs of government, deciding how and to what degree legislation will be enforced, dealing with emergencies, waging wars, and in general fine-tuning policy choices in the implementation of broad statutes. As the head of state and head of government of the United States, as well as commander-in-chief of the United States Armed Forces, only the president of the United States can issue an executive order.

https://en.wikipedia.org/wiki/Executive_order

‘Departments’ such as the Department of Energy, the Department of Transportation, the State Department etc. are under the umbrella of the Executive Branch. Each Department has a Secretary. Secretary of Health and Human Services, Secretary of Defense, Secretary of Urban Development etc. The Secretaries act as liasons for their respective department and report directly to the Chief Executive (president). Given the president is Chief Executive he can give orders to the Departments which “they have to follow” provided they are not illegal or are beyond the department’s budget. These issues, in principle, would be handled by the Judicial and Legislative branches respectively.

All that said, since the president is “in charge” of the Departments he can order them to do whatever he wants in addition. Typically, the president “tells” the Departments what he “wants” done and they will address that issue. An Executive Order is more forceful.

From a constitutional perspective, the problem with Executive Orders and Departments is that they aren’t addressed at all. Constitution establishes the existance of the branches of goverment and lays out general rules, but it doesn’t have anything to say about the structure of the executive branch or even how many judges are on the Supreme Court.

The only way executive orders can be addressed is by law. The legislative branch would need to write amd pass it with 2/3 majority vote to bypass a certain presidential veto.