He's qualified.
"It is not necessary that a man should be born in this country, to be 'a natural born citizen.' It is only requisite that he should be a citizen by birth, and that is the case with all the children of citizens who have ever resided in this country, though born in a foreign country."
- James Bayard, A Brief Exposition of the Constitution of the United States (1834)
Bayard's exposition, including his comments on Presidnetial eligibility, were approved by "The Great Chief Justice" of the US Supreme Court John Marshall, by legendary Supreme Court Justice Joseph Story, and by the almost-as-famous Chancellor James Kent - no less than three of our greatest early legal experts. It was also approved by "other distinguished jurists" as well.
These men knew the Founding Generation, and they knew what they meant when they wrote "natural born citizen."
Cruz is eligible.
Well then... there you have it. BTW, thanks for taking the time to look that up.
LLS