The 23-year-old, who came second in the Tour of Britain, continued momentum from success in the time trial title at the British National Road Championships in Lincolnshire, having also finished on the podium for the road race.
Hayter – an Olympic silver medallist in the madison – had already collected a bronze from the team pursuit event earlier this week in Roubaix.
The British rider dominated his qualifying heat before winning the first two main events on Saturday afternoon, keeping clear of a crash in the latter stages of the scratch race.
In the elimination race, Hayter stayed at the front, eventually finishing fourth, which saw him lead the standings heading into the final event.
“The way that last race went, it was quite tight at the start, but I knew if I scored well in the first few sprints and had a little gap it would make life a lot easier for me, and I pretty much just rolled off,” said Hayter, the first British rider to win men’s world omnium gold since Ed Clancy in 2010.
“The race was going really hard and people were tired, but I just kept the pressure on and once I was off I committed and took the lap and then ended up taking another, so yeah, amazing.”
Hayter, who is also set to compete in the madison on Sunday, added: “I’ll feel it tonight, but I kind of felt better throughout the day to be honest, so I’m feeling good for tomorrow.”
Earlier, Archibald teamed up with Neah Evans in the women’s madison to win a third medal of the week.
The British duo claimed two points in the final sprint to finish one ahead of the Italians, as Dutch pair Amy Pieters and Kirsten Wild took gold with France’s Clara Copponi and Marie Le Net in second.
Evans said: “A worlds bronze medal is very special. It was a really hard race from the gun, really good race, obviously we’re slightly disappointed.
“But I think there’s a lot to be proud of today and some points we’re looking to improve on, and I think the future is going to be really bright for us.”
Elsewhere, Joe Truman and Hamish Turnbull reached the 1/8 finals of the men’s sprint, while Megan Barker and Ella Barnwell finished ninth and 10th respectively in qualifying for the women’s individual pursuit on their elite world championships debut.
The championships conclude on Sunday, with the women’s points race, men’s sprint, men’s madison, women’s keirin and men’s elimination event.
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