Like statutes or regulations promulgated by government agencies, executive orders are subject to judicial review, and may be struck down if deemed by the courts to be unsupported by statute or the Constitution.
There is no constitutional provision nor statute that explicitly permits executive orders. The term "executive power" Article II, Section 1, Clause 1 of the Constitution, refers to the title of President as the executive. He is instructed therein by the declaration "take Care that the Laws be faithfully executed" made in Article II, Section 3, Clause 5, else he faces impeachment