With a voter turnout of 69.5%, 93,272 votes went to the option to leave, with 44,115 voting to remain.
Nationally, Britain voted to leave the EU - 52% to 48%. Yorkshire and the Humber gave one of the highest eurosceptic results in the country, with 57.7% of people backing Leave.
Prime Minister David Cameron, who announced that he would step down following the result, said: "The will of the British people is an instruction that must be delivered. It was not a decision that was taken lightly, not least because so many things were said by so many different organisations about the significance of this decision.
"So there can be no doubt about the result."
John McDonnell MP, Labour's Shadow Chancellor, said: "People will be waking up this morning to turmoil in the markets and the pound crashing, and fearing the emergency budget the Chancellor threatened to hike their taxes and cut public services.
"The Government must now take steps to stabilise the economy, and to protect jobs, pensions and wages."
Paul Luen, CEO of Martek Group, the Rotherham success story which exports safety and environmental monitoring systems around the globe, welcomed the result.
Truly momentous day. Well done 52% of Britain for believing in ourselves and having Vision. Let’s TAKE BACK CONTROL! 👍😎— Paul Luen (@paulluen) June 24, 2016
Tom Fripp, managing director at Fripp Design and Research, an innovative company based on the Advanced Manufacturing Park (AMP) in Rotherham, was not so happy with the way people voted.
David Greenan, managing director at Newburgh Precision, the Rotherham manufacturer that has been building exports back up following the downturn in the global oil & gas market, was more balanced.
Just as i was thinking there was light at the end of the tunnel the tunnel got longer but maybe the light will be brighter.#ukmanufacturing— David Greenan (@DavidGreenan) June 24, 2016
Cllr. Chris Read, the leader of Rotherham Council said that there was "nothing to do but hope."
Sterling dropping like a stone, FTSE expected to fall, country divided, years of negotiation ahead. Nothing to do but hope.— Chris Read (@christophe_read) June 24, 2016
Rotherham's MP, Sarah Champion, said she would continue to fight for Rotherham's business.
Well my job now is to fight to make sure #Rotherham people & businesses get the best possible deal going forwards— Sarah Champion MP (@SarahChampionMP) June 24, 2016
The University of Sheffield, whose Advanced Manufacturing Research Centre (AMRC) has secured millions in EU funding for facilities and research projects in Rotherham, said that leaving the EU will not happen overnight and that "there will not be any immediate material change" to the UK university sector's participation in EU programmes such as Horizon 2020.
Sir Keith Burnett, Vice-Chancellor of the University of Sheffield, said he was "gutted" at the decision, adding: "We are setting our course in a new direction, sailing into uncharted waters. I am not alone in wondering what it might mean. Academics engaged in projects with other EU universities drawing on EU funding wonder about the future of their work."
Tata, the Indian company that has put its UK steel assets up for sale and last week issued a memo to staff at its UK steel sites on the importance of the European market, said in a statement: "Tata has been operating in the UK since 1907 and remains committed to delivering long-term value for all its stakeholders. There are currently 19 independent Tata companies in the UK, with diverse businesses. Each company continuously reviews its strategy and operations in the light of developments, and will continue to do so. Access to markets and to a skilled workforce will remain important considerations."
Images: European Union