Several people were involved, but the key figure most often credited is James Madison, who is known as the “Father of the Constitution” for his central role in drafting and shaping the document during the 1787 Constitutional Convention. The final polished wording of much of the text was prepared by the Convention’s Committee of Style, led by Gouverneur Morris, who actually wrote much of the final language that appears in the document.

If you mean “who literally hand‑wrote the parchment you see in the National Archives,” that was Jacob Shallus, a clerk hired to engross (carefully copy) the agreed‑upon text onto the official parchment copy.