"upon these words" is correct and usable in written English.
You can use it to refer to words that have been spoken or written by someone. For example: "The audience was captivated by the speaker's impassioned speech, so much so that the room fell silent upon these words."
I came upon these words written by a young Frenchman on a French Web site dedicated to remembering D-Day: "For all those who fell on 6 June 1944, a word: thank you".
Went to Mr Gunning's chapel at Exeter House, where he made a very good sermon upon these words:— "That in the fulness of time God sent his Son, made of a woman," &c.; showing, that, by "made under the law," is meant his circumcision, which is solemnized this day.
As we reflect upon these words, lament the sin of racism personally and publicly.
Some people might stumble upon these words and merely laugh, turn the page, and move on.
As I told 60 Minutes, 'It must be in the wrist!'" Some people might stumble upon these words and merely laugh, turn the page, and move on.
As I reflect upon these words and think of the furor that has erupted over the "Ground Zero Mosque" proposal, as the Chairman of The Foundation Of Ethnic Understanding, I am appalled.
If Poland refuses, it is upon her that the responsibility for a conflict will fall and not upon Germany". These words, which I must insist were quoted to me in a strictly confidential manner, seem to me to sum up fairly well the present state of the German-Polish tension.
My mum was mortified upon hearing these words.
"Upon hearing these words," Woodley writes, "I was immediately inspired to cut my own hair off with abandon".
Indeed, 112 years ago, Sen. Leland Stanford reminded the very first class of Stanford students of that necessity with these words: "Upon the individual efforts of each of you mainly depends his or her future success in life.
Then did thy mother's husband take the barley for sprinkling, and began casting it upon the hearth with these words, "Ye Nymphs, who dwell among the rocks, grant that I may often sacrifice with my wife, the daughter of Tyndareus, within my halls, as happily as now, and ruin seize my foes!".
