According to the Historychannel.com, Delaware was the first to ratify the constitution on 12-7-1787 and Vermont the last on 1-16-1791 leading congress to formally adopt the constitution.
While the above is accurate in how it is described, the answer to the question is a single date; and the ratification of the Constitution of the USA was January 16th, 1792.
Additional, slightly off topic, but never-the-less important is the following:
Prior to that we had the at least two other governments from the start of the Revolutionary War against the Crown of England, which, (rightfully from their perspective), considered the our revolution to be the act of traitors; and on top of that you had a division between those who supported the revolution and break with Great Britain, known as Tories and those who supported it.
Many people like to point to those prior documents as examples of what our Founding Fathers' had intended, but the fact remains that in the end the document crafted and ratified that we look to for guidance in government is the one they ratified in 1792; and anything before that has no place in politics and political discussions, though should be taught and understood for historical reasons.
The original 13 states were (in order): Delaware (ratified the Constitution on December 7, 1787) Pennsylvania (ratified the Constitution on December 12, 1787) New Jersey (ratified the Constitution on December 18, 1787) Georgia (ratified the Constitution on January 2, 1788) Connecticut (ratified the Constitution on January 9, 1788) Massachusetts (ratified the Constitution on February 6, 1788) Maryland (ratified the Constitution on April 28, 1788) South Carolina (ratified the Constitution on May 23, 1788) New Hampshire (ratified the Constitution on June 21, 1788) Virginia (ratified the Constitution on June 25, 1788) New York (ratified the Constitution on July 26, 1788) North Carolina (ratified the Constitution on November 21, 1789) Rhode Island (ratified the Constitution on May 29, 1790)
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