According to most historians, the engrossed Declaration of Independence was primarily signed on August 2, 1776.
This date differs from July 4, the date Congress adopted the Declaration and the date celebrated as Independence Day. The formal parchment had to be prepared after the text was approved, and not every delegate was present or authorized to sign at the same time.
The signing was not a single event involving every name at once. Most delegates signed on August 2, while some signed later. Historical accounts also record disagreement among early participants about whether all signatures were added on July 4.
The distinction matters because “adopted,” “engrossed,” and “signed” describe different stages. July 4 marks congressional approval of the declaration; August 2 is the generally accepted date for the main signing of the final parchment copy.