Actually no.
Congress has to give the POTUS this power called "Presidential Reorganization Authority."
So far Congress has not that. This is why his (probably) illegal EA's "reorganizing" congressionally authorized and funded agencies are subject to legal challenges.
Between 1932 and 1981, Congress periodically delegated authority to the President that allowed him to develop plans for reorganization of portions of the federal government and to present those plans to Congress for consideration under special parliamentary procedures. Under these procedures, the President’s plan would go into effect unless one or both houses of Congress passed a resolution rejecting the plan, a process referred to as a “legislative veto.” This process favored the President’s plan because, absent congressional action, the default was for the plan to go into effect. In contrast to the regular legislative process, the burden of action under these versions of presidential reorganization authority rested with opponents rather than supporters of the plan. In 1984, the mechanism was amended to require Congress to act affirmatively in order for a plan to go into force. This arguably shifted the balance of power to Congress. The authority expired at the end of 1984 and therefore has not been available to the President since then.
On January 13, 2012, President Barack Obama announced that he would ask Congress to reinstate so-called presidential reorganization...
www.everycrsreport.com