The Welshman's triumph is the sixth by a British rider since 2012 and saw him beat his team-mate and compatriot Chris Froome, the victor of four of the past five instalments of the three-week stage race.
Following Thomas' convincing display in the final mountain stage Friday, the Team Sky rider knew that he just had to finish within 2:04 of Dumoulin to secure the overall win. I encouraged him to get out and get it out of his system, in a way.
"The dream was always to participate, and that dream came true 11 years ago", Thomas said.
In 2012, he was not riding the Tour when Wiggins, another track cyclist turned grand tour ace, became the first Briton to win the race.
"It won't really sink in probably for a few months". Right now it's like a whirlwind.
"I didn't think the course was too technical but then every corner seemed like a 180 degree turn".
The 51 seconds were useful, but Thomas found other ways to pick up time on Froome and everybody else throughout the race.
His closest rival at the start of the day, Tom Dumoulin, won the stage by one second from Chris Froome, but with Thomas only 14 seconds back the Welshman had more than enough in hand.
"I've not got a good track record with speeches so I'll keep it short", Thomas said on the podium.
"He didn't make any mistakes, he was never put into trouble by anyone - including me - in the mountains or in any stage".
Cosmo Catalano relives the crucial Stage 19 with Geraint Thomas in prime position to win his maiden Tour de France after he retained the overall leader's yellow jersey in a lively stage won by Slovenian Primoz Roglic.
"It's incredible. I didn't let myself think about this time".
Team Sky sat up together, chinking glasses, smiling and laughing for the cameras.
While Dumoulin is the time trial world champion, Thomas is quite capable in the discipline and acknowledged he should be able to protect his advantage.
Team Sky principal Sir Dave Brailsford said: "We're just pretty emotional".
Thomas, who was cheered during the podium ceremony, also had a message for riders aged 5-18 at the Maindy Flyers Cycling Club in Wales.
"It was my dream to win a stage, now I've won two and I've got the polka dot jersey on my shoulders". If people tell you it can't be done, keep going and believe in yourself.
Thomas and the peloton will complete the arduous, three-week race with a 72-mile ride that ends on the Champs Élysées.
Pundits agreed that the 21-year-old Egan Bernal, who produced some unbelievable work in the mountains for his leaders on his Tour debut, would probably soon win the race. However, the prospect of Moscon avoiding the sack from Sky looks slim, following previous misdemeanours which have left him on his final warning from Sky. But this was surely the easiest stage of the lot: 116km of procession more than competition, neutralised by a traditional truce, from the Parisian suburb of Houilles to the Champs-Élysées.