Here's what the constitution has to say about Presidents and citizenship:
No Person except a natural born Citizen, or a Citizen of the United
States, at the time of the Adoption of this Constitution, shall be
eligible to the Office of President; neither shall any Person be
eligible to that Office who shall not have attained to the Age of
thirty-five Years, and been fourteen Years a Resident within the
This was clearly meant to grandfather in people who were citizens at the time, but eventually transition to Presidents having to be natural-born citizens.
Washington, as you say, was technically born an Englishman in Virginia Colony, but was a US citizen in 1789 when the Constitution went into effect.
Martin Van Buren (8th President) was born in New York in 1782. This was after the Declaration of Independence, but while the USA was operating under the Articles of Confederation. This arguably makes him the first "natural born" US president. However, as he also qualified under the "Citizen of the United States at the time of the adoption of this Constitution" phrase, its not an issue anyone would ever have to clarify.
John Tyler (10th President) was born in Virginia in 1790, which makes him the first US president born after the Constitution was ratified.
Incidentally, Zackary Taylor (12th President) was the only president after Tyler to have been born before the Constitution went into effect. However, like Van Buren, he was born in the US under the Articles of Confederation, so was technically a "natural born Citizen" too.