The three-time world champion and world record holder, silver medallist at the Tokyo Games, timed an Olympic record of 26min 43.14sec for victory.
That beat the previous best of 27:07.17 set by Ethiopian great Kenenisa Bekele at the 2008 Beijing Games.
Ethiopia's Berihu Aregawi edged fast-finishing American Grant Fisher by two-hundredths of a second to take silver in 26:43.44.
Cheptegei admitted to having been inspired by Bekele's Beijing triumph.
"It's the dream of young people to achieve what they want to achieve in life," said Cheptegei.
"Barely 16 years ago when I was watching the great Kenenisa Bekele win in Beijing, it was something that grew in my heart.
"I said, one day, one time, I want to be Olympic champion."
Cheptegei, 27, added: "I've wanted this for a long time. When I took silver in Tokyo, I was disappointed. I wanted just to win the 10,000m.
"It took a lot of courage. It's really amazing, this one was still missing. Three times world champion, now I can add the Olympic title to this."
The first surge came after just two laps of the 25-lap race, defending champion Selemon Barega and Ethiopian teammate Yomif Kejelcha accelerating away to split the field.
The 25-strong field dissipated but all runners held in there.
Aregawi had his turn after Kejelcha as the Ethiopian trio dictated the pace in front of a noisy near-capacity 69,000 crowd at the Stade de France in perfect warm conditions.
Cheptegei and Jacob Kiplimo saw their own team tactics take a dent when Martin Magengo Kiprotich fell off the pace early on.
Aregawi and Kejelcha again increased the rhythm through the halfway stage, the main pack now cut to 15.
Barega was back at the helm with 10 laps to run, Canada's Mohammed Ahmed and Kenya's Benard Kibet muscling their way through to sit on Kejelcha's shoulder.
As Cheptegei and Fisher made their way up through a bunching pack, Kejelcha was again on hand to offer a spurt of acceleration.
Into the last kilometre, Aregawi took up the running, but the race promised a pulsating finish as the pack of 12 all clung on.
Just before the bell rang for the final 400 metres, Cheptegei surged to the front and the race to the line was on.
Ahmed followed, Fisher fell off the pace, but made a remarkable recovery to medal.
There was no coup de grace for Barega, however, as Cheptegei -- who also won 5,000m gold in Tokyo -- held on for victory in the first medal event of the track and field programme at France's national stadium.
Barega eventually finished seventh in 26:44.48, one spot behind Kejelcha, with Ahmed taking fourth and Kibet fifth.
