The Continental Congress approved the final wording of the Declaration of Independence on July 4, 1776. They'd been working on it for a couple of days after the draft was submitted on July 2nd and finally agreed on all of the edits and changes.
July 4, 1776, became the date that was included on the Declaration of Independence, and the fancy handwritten copy that was signed in August (the copy now displayed at the National Archives in Washington, D.C.) It’s also the date that was printed on the Dunlap Broadsides, the original printed copies of the Declaration that were circulated throughout the new nation. So when people thought of the Declaration of Independence, July 4, 1776 was the date they remembered.
In contrast, we celebrate Constitution Day on September 17th of each year, the anniversary of the date the Constitution was signed, not the anniversary of the date it was approved. If we’d followed this same approach for the Declaration of Independence we’d being celebrating Independence Day on August 2nd of each year, the day the Declaration of Independence was signed! by Constitutionfacts.com