Ms Freeman also announced twice-weekly testing for all patient-facing NHS workers by the end of the year, and for all designated care home visitors over Christmas.
There will be assessments of a routine asymptomatic testing programme for school staff after Christmas.
Testing for home carers will begin in mid-January.
The mass testing site in Johnstone, Renfrewshire, will offer lateral flow tests even to those without symptoms, and will have the capacity for 12,000 tests a week.
Johnstone has one of the highest case numbers per 100,000 in Scotland.
Testing will also be increased next week in Glasgow City, Renfrewshire, East Ayrshire, South Ayrshire, and Clackmannanshire, with up to six extra mobile testing units and 20,000 home test kits.
By the start of December testing will be extended to emergency departments, acute assessment centres, maternity units, and emergency mental health units.
By mid-December all medical and surgical elective admissions will be tested.
Twice-weekly testing will be brought in for all patient-facing NHS staff from the end of December, with a complete rollout by the end of the month.
"The scale of that challenge is not to be underestimated: NHS Scotland employs more than 170,000 people and although not all are in patient-facing roles, the number who are is considerable,” said Ms Freeman.
From December 7, designated visitors to 12 care homes across four local authority areas will be offered a lateral flow test on the day of the visit. These return results in 30 minutes, so that if a test is positive family members can self-isolate.
This will be extended to other homes in seven more local authority areas before December 21, with rollout completed in early February.
In the meantime those homes not part of the initial rollout will be offered PCR testing in the weeks beginning 21 and 28 December and January 4, to allowed loved ones to visit over the Christmas period.
From mid-January testing will be extended to home carers, including permanent and visiting staff and personal assistants in a person’s home, covering residential settings, sheltered housing and day care.
From the school return in January the Scottish Government will look at developing a programme of asymptomatic testing of school staff.
“With the plans that I have set out, we will move to testing hundreds of thousands of people without symptoms, in order to actively find the virus, and, with the continuing co-operation of people across Scotland, to prevent and break down chains of transmission before Covid-19 can cause the harm of which we know it is capable,” said Ms Freeman.
Scottish Labour health and social care spokessperson Monica Lennon welcomed the announcement but criticised the SNP for not expanding testing sooner.
“SNP ministers were warned months ago to test all hospital workers routinely to help slow virus transmission. Scottish Labour won a vote in Parliament earlier this month to begin ‘immediate’ testing of NHS and healthcare staff but today the SNP government announced that it will be December before this happens,” she said.
“For at-home care workers, they will have to wait until March – a full year on from the start of the pandemic.”