While others had attempted to measure it before, Rømer's method was the first to be considered truly successful. He observed the eclipses of Jupiter's moon Io and noticed that the timing of the eclipses varied depending on the Earth's position in its orbit around the Sun. He deduced that this was due to the time it took light to travel the varying distances between Earth and Jupiter.
However, it's important to note that Rømer's measurement was not a direct measurement, but rather a calculation based on observations and assumptions.