That's an interesting question. To make a distinction between "popular" and "professional" is the kind of thing that requires several prerequisites. You need to have a sufficiently literate "populace" who consumes books for more or less entertainment. You also need to have a field that has "professionalized," e.g., has become somewhat specialized in who is considered a "professional" versus an "amateur."

I can't speak for popular history, but for popular science these two distinctions basically show up in the English-language literature in the mid-19th century. It wasn't an overnight sort of thing, but you started to have people who thought of themselves as the "serious scholars" (who were often attached to academic institutions, or were inducted to members to academic societies), and then you had the people who were writing for the literate masses. So one can contrast the style of book (and author) in Robert Chambers' anonymously published Vestiges of the Natural History of Creation (1844) with the style of book (and author) as exemplified by Charles Darwin's On the Origin of Species (1859). Both are books with ambitious theories about evolution and the natural world, but Chambers' book was decidedly of a "popular" bent, and was treated with scorn and disdain by the "professionals" even while it was read eagerly by the British public (and indeed, there were more copies of Vestiges in circulation in England than there were copies of Origin throughout Darwin's lifetime). Darwin's book was written to be readable by a literate public (it is not consumed by jargon), and indeed was read by them (and discussed by the "literati"), but was clearly aimed at being a work of "serious" natural history, with copious footnotes, caveats, and careful attempts to make clear the evidence being discussed. And where Chambers was a Scottish publisher who worked anonymously, Darwin was already well-known in scientific circles (for his book on the Beagle voyage, and several of his other scientific contributions), and was a member of the Royal Society, Royal Geological Society, etc. I am just using these two as examples (prominent ones, to be sure); again, nothing comes out of nothing, so there are precursors if you go back earlier, even to the Enlightenment. But probably not a whole lot earlier than that (e.g., Robert Hooke's Micrographia was clearly not a work of "popular" science but it could be read and understand by the literate people of his day, not merely "natural philosophers").

So when did "history" professionalize? Around the same time — typically historians point to Leopald von Ranke as the scholar who creates the "modern" approach to history, which is to say, the "professionalized" approach with a definable methodology, standard educational path, and common expectations about what kind of result you'd want to get out of historical research. It is not surprising to find this overlapping with the popular science notions; the 19th century is when European academic study became much more "professionalized" under the modern definition of it, with increased specialization, increased importance of academic institutions, the proliferation of "modern" scientific journals (as opposed to the relatively loose "proceedings" that were characteristic of the early modern period), and so on.

I'm no expert on Gibbon's reception but I suspect that his contemporaries would not even understand your question — there was no "academic history" and there was no "popular history." There were works of history, some learned, some full of errors and ignorance. To make a distinction between "serious" and "non-serious" history on the basis of audience is probably not how they would have thought of things, in part because there was at that time very little true "popular" audience to speak of (printing was not yet so cheap as it would become, literary not yet so common — if you could own a copy of the book and read it, you were probably the target demographic). But I am certainly speculating a bit here.