First, on common law:
After the English civil wars of the mid 17th century and the return of a number of English subjects who had departed the realm during the wars, an Act of Parliament determined that all children who, during the period of the wars, “were born out of his majesty’s dominions, and whose fathers or mothers were natural-born subjects of this realm,” were themselves natural-born subjects. (The act was cited in the landmark 1898 Supreme Court case United States v. Wong Kim Ark that ruled that the children of non-citizen lawful permanent residents born in the United States are automatically U.S. citizens.)
. . .
A bit further on, [William Blackstone] specifically recognizes that the children born abroad of natural-born English subjects are themselves natural-born subjects. And a few pages after that, he recited several acts of parliament that established the broad proposition that children born abroad to English subjects were themselves natural-born subjects “in allegiance to the king.”[emphasis added]
Then on U.S. statutory law:
The requirement in Article II that one be a “natural-born citizen” in order to be eligible for the presidency simply means that one be a citizen from birth, rather than subsequently becoming a citizen by later naturalization.
Moreover, this was the understanding of the clause given by the very first Congress in a bill passed in 1790 and signed into law by President George Washington: “Children of citizens of the United States, that may be born beyond the sea, or out of the limits of the United States, shall be considered as natural-born citizens.”[emphasis added]H/T Mark Levin