This happened gradually and no specific person or date can be stated.
Ancients divided day into equal parts and night into equal parts. So day and night hours were unequal. Of course they realized this. To measure time in the ancient world, there were sundials and water clocks. In the Hellenistic times there were sophisticated water clocks showing unequal hours during the day and night.
With the invention of mechanical clocks, gradually people started to measure time
by mechanical clocks, but this was a slow process. They begin to spread in 14th century, and first ones were tower clocks in the cities. I suppose in the villages, people still used Sun and unequal hours. The standard of clocks was
based on the revolutions of Sun (one full revolution=24 hours).
However, astronomers realized very long ago (in the ancient times) that revolutions of Sun are also not equal: even if you divide day+night (one complete revolution of Sun) into equal parts, these hours will be unequal because of the equation of time (see "equation of time" in Wikipedia).
So the time unit should be based on the revolutions of stars, which is more uniform.
For people other than astronomers,
this was clearly realized and described only in the middle of 18th century,
with the publication and use of the Nautical Almanac by Nevil Maskelyne.
Again attempts were made to produce sophisticated mechanical clocks which would
show "true" solar time, that is unequal hours. Only with the spread of precise
pocket watches, people started using "equal hours" defined astronomically, as the "mean solar time", that is the revolutions of the starry sky was taken as the standard.
In the end of 19th century scientists realized that any hours defined astronomically are also slightly unequal. It was J. C. Maxwell who first proposed to base the definition of time units on physical processes (frequency of certain radiation) instead of astronomy. His proposal was adopted in the beginning of 20s century. So the modern definition of hour is not related to the
revolutions of the Earth at all, and the hour is defined as 3600 seconds, and the second, the fundamental time unit, is defined as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom". The final refinement of this definition, specifying the conditions under which this radiation has to be measured was established in 1999, if you wish a date.
Of course the corrections made in 20th century are too small to concern our daily life. So for the hour used in daily life, the standard is a watch, and
it spread slowly with the spread of non-expensive watches in the beginning of 20s century.
The described process can be summarized as follows: people use some natural process which is thought to be uniform, to measure time. With the development of knowledge, they discover that the process is in face not exactly uniform. They find a new process, which is first used by scientists, but then its use gradually spreads. And this story repeats and lasts as long as our civilization lasts.