In part, James Madison and the Virginia delegates wrote the Virginia Plan while in Philadelphia waiting for the other delegates to the Constitutional Convention of 1787 to arrive. The Plan became the starting point in the debate regarding how to create a new, more adequate structure of government than the Articles of Confederation.

William Paterson created the New Jersey Plan largely as a rebuttal to the Virginia Plan. The New Jersey Plan maintained a governmental structure that was closer to the government under the Articles of Confederation, strengthening the central government significantly but giving every state equal representation in the national congress.

Roger Sherman wrote the Connecticut Compromise, which combined the two plans by creating a bicameral legislature with different representations in the two houses. James Wilson suggested the Three/Fifths Compromise which addressed the question of how to count slaves when figuring the populations of the states.

There were other plans fron such as Hamilton and Pinckney. Input from all sources was debated and discussed through the summer of 1787. During the early fall,

the Committee of Style and Arrangement, headed by Gouverneur Morris, and including Hamilton, William Samuel Johnson, Rufus King, and Madison, produced the final version, which was submitted for signing on September 17. Morris is credited, both now and then, as the chief draftsman of the final document, including the stirring preamble. (Wikipedia.com, eNotes.com)

Who wrote the United States Constitution?

No one person wrote the United States Constitution all by himself.  We do not even know who wrote any particular section of the document.  If your instructor expects you to actually give a name, it is likely that you are supposed to give James Madison as your answer.  Madison is often called the “father of the Constitution,” but this does not mean that he actually wrote the document.

As you can see in the link below from the US government archives, no single person is credited with writing the Constitution.  People sometimes say Madison did and sometimes say that Governor Morris did.  However, experts are not convinced.  As the link says,

The actual literary form is believed to be largely that of Morris, and the chief testimony for this is in the letters and papers of Madison, and Morris's claim. However, the document in reality was built slowly and laboriously, with not a piece of material included until it had been shaped and approved. The preamble was written by the Committee of Style.

So, we have to say that no single person wrote the US Constitution.  If you do have to give a name, I would suggest that you check to see if your textbook gives an answer to the question.  If so, that is probably the name your instructor expects you to give.