I've also answered the cross-posted version of this question on the Christianity Stack Exchange.
During papal coronations, these words are spoken to the pope while a cloth is burned in front of him. Janos M. Bak interprets:
Pater sancte, sic transit gloria mundi [...] is supposed to remind the pontiff of the temporality of even his power.
In that vein, though your literal translation is on track, perhaps a more idiomatic rendering would be "worldly glories are fleeting."
This is a common biblical theme (see my parallel answer and passages like James 1:9–11 and 4:14), but the statement is not a direct biblical quote. Still, its language is reminiscent of the Vulgate's in several places, particularly Matthew 4:8 and 1 John 2:17.
First, Matthew 4:8, where Satan tempts Christ by showing him the kingdoms of the world:
iterum adsumit eum diabolus in montem excelsum valde et ostendit ei omnia regna mundi et gloriam eorum (Vulgate)
Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their glory. (ESV)
And 1 John 2:17:
et mundus transit et concupiscentia eius qui autem facit voluntatem Dei manet in aeternum (Vulgate)
And the world is passing away along with its desires, but whoever does the will of God abides forever. (ESV)
Reliance on the Vulgate, of course, makes sense, given its ubiquity in the medieval and early modern church. If Thomas à Kempis is the originator (o quam cito transit gloria mundi), or even if he isn't, it's natural that this phrase, given its Christian context, would correspond in some ways to biblical language.