The event caters to diverse interests, including medicine and emerging career paths
The 23-year-old from Perth helped his country set a new world record for the men's team pursuit in a gold-medal winning performance.
Half an hour later, he claimed the men's scratch title.
Australia also clinched the women's team pursuit title.
Welsford, Kelland O'Brien, Alexander Porter and Leigh Howard claimed gold over their British rivals in the team pursuit final.
"The tactics were simple: I let the others make all the effort and I simply positioned myself in the peloton and then gave it my all in the last two laps," said Welsford.
The four-man team took victory in the 4km event in a time of 3 min 48.012 sec, more than a second inside their own previous record set last year.
It was a 13th world title in men's team pursuit for Australia.
For Britain's Ed Clancy, it meant a world silver medal to add to his three Olympic titles in the discipline.
Australia had set the previous world record of 3min 49.804sec on home ground at the Commonwealth Games in 2018.
Denmark claimed the bronze medal at the expense of Canada.
Welsford then added the scratch title, the first by an Australian in 17 years at the championships.
Finals results
Women's team pursuit
Australia (Annette Edmondson, Amy Cure, Ashlee Ankudinoff, Georgia Baker) 4:14.333
bt Great Britain (Laura Kenny, Katie Archibald, Elinor Barker, Ellie Dickinson) 4:14.537
3rd place:
New Zealand (Rushlee Buchanan, Bryony Botha, Holly Edmondston, Kirstie James) 4:16.479
bt Canada (Allison Beveridge, Ariane Bonhomme, Annie Foreman-Mackey, Georgia Simmerling) 4:20.327
Men's team pursuit
Australia (Sam Welsford, Kelland O'Brien, Leigh Howard, Alexander Porter) 3:48.012 (new world record)
bt Great Britain (Ethan Hayter, Ed Clancy, Kian Emadi, Charlie Tanfield) 3:50.810
3rd place:
Denemark (Lasse Hansen, Julius Johansen, Rasmus Pedersen, Casper von Folsach) 3:51.804
bt Canada (Derek Gee, Michael Foley, Adam Jamieson, Jay Lamoureux) 3:56.382
Men's scratch
1. Sam Welsford (AUS) 17:12, 2. Roy Eefting (NED), 3. Thomas Sexton (NZL), 4. Christos Volikakis (GRE), 5. Rui Oliveira (POR), 6. Matt Walls (GBR), 7. Mauro Schmid (SUI), 8. Guo Liang (CHN)
Men's kierin
1. Matthijs Buchli (NED), 2. Yudai Nitta (JPN), 3. Stefan Botticher (GER), 4. Matthew Glaetzer (AUS), 5. Jack Carlin (GBR), 6. Sebastien Vigier (FRA)
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