The modern research PhD resulted from the German invention of the modern research university in the early 19th century. The prototype of the research university was Universität zu Berlin, officially opened in 1810 (but teaching had started already in 1809), which was renamed Friedrich-Wilhelms-Universität zu Berlin (1828-1945), and is today Humboldt-Universität zu Berlin, after Wilhelm von Humboldt who is essentially the inventor of the modern research university. I don't know for sure when Universität zu Berlin conferred its first PhD, but I've seen 1810 claimed in passing (e.g., Lybeck, 2019). By 1815, they were attracting foreign students into their PhD program.

As the research university was seen as a successful and productive innovation, other countries followed. The first research PhDs in the USA were awarded by Yale in 1861 (Rosenberg, 1961), with Johns Hopkins becoming the first established-as-a-research-university university in the US in 1876. More conservative England awarded its first research PhD in 1920, and Australia in 1949.

The PhD degree itself is far older than the modern research PhD (and we can note the existence of non-research coursework-only PhDs in some countries today). As a degree awarded by universities, it goes back to Medieval universities. The traditional organisation was in four faculties: Arts, Law, Medicine, and Theology, with Arts providing the basic study and the other three advanced professional training. Depending on the university and faculty, the degree awarded would be a doctorate or master's degree. Paris and the universities patterned after it preferred Master, and Bologna and its derivatives preferred "Doctor". The two were essentially equivalent, both meaning "teacher" and the degrees being licenses allowing the holder to teach. Oxford and Cambridge appear to have introduced a long-standing tradition of awarding doctorates in the professional faculties of Law, Medicine, and Theology - and these degrees (JD, MD, DD, and the variants thereof) are still with us - and master's degrees in Arts. Where the degree was in Arts, "philosophy" was sometimes used as a synonym for arts. A combined doctorate/master's degree was also awarded, such as Magister Artium et Doctor Philosophiæ or Doctor Philosophiæ et Liberalium Artium Magister (Burns, 1907; Ridder-Symoens & Rüegg, 2003b).

"Doctor Philosophiæ" existed before this, but as a job description rather than an awarded degree. It simply means "philosophy teacher", and a teacher of philsophy would have been called a doctor or magister. With the advent of universities in Europe, the universities established a monopoly on these titles and their award (Ridder-Symoens & Rüegg, 2003a).

References:

Burns, J. (1907). "Master of Arts". In The Catholic Encyclopedia. New York: Robert Appleton.

Lybeck, E., "Ajurisdiction", Theory and Society (2019) 48: 167. https://doi.org/10.1007/s11186-018-09337-x

Hilde de Ridder-Symoens, Walter Rüegg (2003a), A History of the University in Europe: Volume 1, Universities in the Middle Ages, Cambridge University Press.

Hilde de Ridder-Symoens, Walter Rüegg (2003b), A History of the University in Europe: Volume 2, Universities in Early Modern Europe (1500-1800), Cambridge University Press.

Rosenberg, R. (1961). "The First American Doctor of Philosophy Degree: A Centennial Salute to Yale, 1861-1961", The Journal of Higher Education 32(7), 387-394. doi:10.2307/1978076