The NHS centre, in Broughton Lane, opens at 10am on Monday, January 25.
People aged 75 and over within a 45 minute drive of the Arena will receive a letter from the inviting them to book a vaccination.
The Arena will be open seven days a week and will be run by Sheffield Teaching Hospitals on behalf of the NHS national vaccination programme.
Husband and wife, Colin and Rita Moss, aged 78 and 79, from Barnsley, will be among the first people to get their vaccination in the new centre.
Rita said: “Colin and I feel really lucky to be getting our vaccines and I’ve never looked forward to getting an injection in my arm as much as I have over the past few days even though I don’t like needles.
"I would definitely encourage others to have their jab when it’s their turn; not just to save themselves, but to save others from this horrible virus too.
"The vaccine is a brilliant, brilliant thing. It will give us peace of mind and make us feel a lot safer but we won’t be changing what we do or who we see in the short term because we know how important it is to keep following the guidelines until more people have been vaccinated.
"I take my hat off to everyone who has helped us get to this point.”
Dr Jennifer Hill, Medical Director (Operations) at Sheffield Teaching Hospitals NHS Foundation Trust said: "GPs, nurses, pharmacists and countless other NHS staff, partners and volunteers are pulling out all the stops to deliver the vaccination programme as quickly as we can across South Yorkshire and Bassetlaw.
"It is tribute to their hard work that we have already vaccinated thousands of our most vulnerable residents.
"The Arena opening today is another step forward in rolling out the vaccination programme and it has been fantastic to see people like Rita and Colin getting their vaccinations and being protected against this awful virus."
Dr Hill added: "We are asking people to help us by not turning up at the Arena unless they have an appointment as we cannot vaccinate people ad hoc.
"The teams at the arena, at our hospitals or GP surgeries cannot make appointments for the Arena and so by calling or turning up turning up it will simply take time away from the staff who are vaccinating and that is the last thing anyone wants to happen.
"As well as NHS colleagues, I would also like to thank the team at the Arena who have been simply amazing. First they supported us to create a drive through blood testing service so that our most vulnerable patients could still have their blood tests safely and now they have been instrumental in our planning for the vaccination programme roll out.”
"Finally a plea that over these next few months, even if you have had your vaccine, you must continue to wash your hands regularly, limit contact with other people unless it is essential and wear a mask when required.
"Our hospitals are fuller than ever before with patients who have COVID-19 and if we are to get control of this awful virus we need everyone to do all they can to limit transmission to others whilst we continue to vaccinate the population.”
-> Yorkshire's vaccination centres praised but concerns for region's rural residents growAndrew Snelling, Chief Executive of Sheffield City Trust, said: “Throughout the pandemic, Sheffield City Trust has worked closely with the National Health Service to provide a range of support.
"We’re very proud of the role Sheffield Arena has played as part of the City’s response; from providing extra storage for equipment to providing a drive-through blood testing facility used by over 50,000 cars.
"As an organisation, our core values are promoting and enhancing the health and wellbeing of communities, so we’re happy to support Sheffield Teaching Hospitals, the NHS and the Government, in being able to provide whatever is required to deliver this vaccination programme.”