The Scottish Event Campus (SEC) in Glasgow could be in operation as a temporary hospital within two weeks, Nicola Sturgeon has said.
The emergency facility will be run by the NHS and could have capacity for more than 1,000 patients.
The first minister confirmed that six more people with Covid-19 have died in Scotland, bringing the total to 47.
A total of 1,563 people were confirmed as having been diagnosed with the virus - up from 1,384 on Sunday.
Meanwhile screening programmes for bowel, breast and cervical cancer have been put on hold in a bid to free up capacity in the health services.
And 10,000 people have come forward to volunteer to help support services and vulnerable people inside the first four hours of the new Scotland Cares campaign.
Exploratory work had been carried out by the army to see if the SEC could be used as a temporary hospital, similar to those being set up in London, Birmingham and Manchester.
Ms Sturgeon said work had begun to initially create capacity for 300 extra beds, but that figure could ultimately rise to over 1,000.
Ms Sturgeon stressed that "we might not need to use the exhibition centre", with 3,000 of the 13,000 hospital beds across Scotland's NHS hospitals currently being kept available for coronavirus patients.
However she said it "makes sense for us to act now to increase hospital capacity further", with the SEC the "best option" for doing this given its proximity to other facilities and transport links.
She said the extra beds there would "initially be for use by those who have been through hospital treatment and are recovering from their symptoms".
Health Secretary Jeane Freeman said the emergency facility would be a hospital staffed by and run by the NHS, "with full clinical and medical infection control standards".
SEC chief executive Peter Duthie said he was "proud to be in a position to help our NHS", adding: "Our teams will support the NHS in the build, security and safe operation of the resource, and continue to express our sincere gratitude for all that they are doing to fight Covid-19."
Work is also ongoing to quadruple the number of intensive care beds in Scotland to 700 - Ms Sturgeon said there were now 108 patients with the virus in intensive care, up 13 from the weekend.
Other measures are also being taken to free up capacity in the NHS, with treatments such as knee and hip operations being put off.
Ms Sturgeon said ministers had now taken the "very difficult" decision to suspend screening programmes for breast, cervical and bowel cancer.
Hundreds of thousands of people take part in these screenings each year, but the first minister said it was important to "maximise" the ability of the health services to deal with the virus over the coming weeks.
The government has also encouraged medical students and retired healthcare staff to volunteer their services to "plug gaps" in frontline services.
Chief Medical Officer Catherine Calderwood said up to 20% of the health workforce could ultimately have to take time off due to illness.
Ms Sturgeon said about 5,000 students or former workers have expressed an interest in filling posts, and said "many will be offered fixed-term employment".
Two weeks before the expected peak in the virus, NHS Scotland is getting ready. They are freeing up staff for the frontline. That lies behind today's decision to suspend screening programmes.
This will be worrying for some patients and it's a difficult balancing act. Contact with health professionals could spread the disease further but could also store up problems for the future.
The decision to announce the SEC in Glasgow as the site of a temporary hospital is also getting more capacity into the system to deal with the coming peak in infections. It's a complex exercise as it's important to keep Covid-19 patients away from others to prevent cross-infection.
Within a fortnight the new hospital could be providing 300 extra beds and this could eventually reach 1,000 beds.
The Scottish government say they are making the decision now to act now, even while hoping they won't need to use it.
Meanwhile police in Scotland have handed out 25 fixed penalty notices to people who were not complying with social distancing rules.
Ms Sturgeon said "the vast majority of people are doing the right thing to protect themselves and the wider community", saying that "by staying at home we can all help slow the spread of this virus and ultimately save lives".
Warning that strict measures could be in place for a long period of time, she added: "I don't want people to have to comply with these measures for a single day longer than is necessary.
"I want to get back to normal in this country as soon as possible. But we need to keep the measures in place for as long as we judge, based on expert advice, and I and others have to ask the public to stick with them."