The double world champion made history for his country by edging out Kazakh Nariman Kurbanov by 0.100 points, with Stephen Nedoroscik of the United States in bronze.
Britain's most decorated gymnast Max Whitlock was deprived a perfect send-off to his decorated Olympic career, finishing fourth.
Whitlock was seeking an unprecedented fourth medal on the same apparatus after golds at the last two Games in Tokyo and Rio, and bronze at London 2012.
He was sitting third until Nedoroscik did enough to take his place on the podium.
McClenaghan crumpled with emotion after his faultless 60-second performance crammed with Russian circles, scissors and handstands, finishing off with a foot-perfect dismount.
The 25-year-old from County Down went into the final as favourite after heading qualifying.
But also with heaps of pressure after falling off the apparatus at the Covid-delayed Tokyo Games three years ago to trail in seventh.
He wasn't about to let this second shot at writing his name in Irish sporting folklore go awry though.
With a score of 15.533 he wept tears of joy as he listened to "Amhran na bhFiann" - the Irish national anthem - with green, white and orange tricolours being waved proudly from the stands by his legion of supporters at the Bercy Arena.
