Voigt, who turned 43 on Wednesday, bettered by 1,415 metres the previous mark of 49.700km set by Ondrej Sosenka of the Czech Republic in 2005 in Moscow. Prior to Sosenka, the record was held by British Olympic champion Chris Boardman with 49.441km.
Those records, though, were on bicycles that had to closely resemble the one used by Belgian great Eddy Merckx for his record in 1972. But now the UCI is allowing records using current track cycling pursuit bikes.
Voigt, who is estimated to have cycled around 850,000 km in his career, said he was stunned by breaking the iconic mark.
"51 kilometres in a hour, it's a lot more than I had imagined," said the Berliner.
"I gave it everything in the last 20 minutes. I knew that I still had the energy, that I was ahead of the mark. I felt euphoric -- it was the last 20 minutes of my sporting career.
"I was super-motivated. Now I am on the list of all the famous names, I am so proud to join the likes of Merckx, Indurain. It's fantastic to finish like this."
In a velodrome full to its 2,000-capacity, Voigt was backed by a raucous rock concert atmosphere with AC-DC and Metallica fuelling his record ride.
Riding a Trek cycle, weighing just 8.15kg, Voigt was 12 seconds ahead of Sosenka's mark after 10km (12 min 01.336sec) and 24 seconds better off after 20km (24 min 03.565sec). He accelerated again in the last quarter of an hour in carving out half a second a lap to stay on course.
UCI President Brian Cookson offered his congratulations: "Jens Voigt's performance was sensational. I'm very happy for him.
"The Hour Record requires a huge physical and mental effort and Jens' performance today sets down a new marker for the challenge. I'm confident that his achievement will have a domino effect: other great riders will resolve to attack one of the greatest challenges in our sport."
In the lead-up to his record attempt, Voigt had already expressed his optimism, noting he "had three weeks of intense preparation," in the lead up to his last professional challenge of his 18-season career.
After competing in a record-equalling 17th Tour de France, Voigt went to the United States to ride at altitude in the lung-busting Tour of Utah and Tour of Colorado. He then completed his build-up to Thursday's event at 450m above sea level at Soleure in Switzerland.
But Voigt admits that his new record may not last long with teammate Fabian Cancellara as well as former Tour de France winner Bradley Wiggins believed to be eyeing the hour record.
"I am under no illusion as to my chances of keeping the record when Fabian Cancellara and other specialists are going to attack it," he said.
"But I like the idea of being able to tell my grandchildren about it when I am 75."
Three most recent best hour performances:
51.115km: Jens Voigt (GER), 18 September 2014 at Granges
49.700km: Ondrej Sosenka (CZE), 19 July 2005 at Moscow
49.441km: Chris Boardman (GBR), 27 October 2000 at Manchester