The by-election follows Harry Harpham’s death from cancer in February.
The hustings was held at the Parkwood Academy in Sheffield last night.
The daughter of a steel worker, Gill is a former librarian and Northern General Hospital worker.
She has served as a councillor in the constituency for more than 16 years.
Gill Furniss said:“I’m deeply humbled to have been selected by members of my home constituency to stand as Labour’s candidate in this by-election.
“It is a by-election none of us wanted but one we must all work hard to win.
“We were all incredibly proud of Harry, and he was proud of Sheffield. Now it falls to me to carry on the work he started.
“In me, Brightside and Hillsborough will have an MP who will fight tooth and nail for the future of our steel industry, pressing every day for the Tories to end their inaction to help companies like Forgemasters, who are so crucial to Sheffield’s economy.
“I’ll fight for our NHS, which finds itself in dire straits financially and with a Tory government determined to sell it off to private companies.
“And I’ll make the case for a comprehensive plan for affordable housing for local people to own and to rent, to end the Tory housing crisis.
“The hard work starts now – I’ll reach out across the whole constituency to win your trust and support.”