The scheme, through which each household in the city can collect five free tests each month until June, was introduced to take over from the government which stopped its provision at the end of March.
Council leader Gerald Vernon-Jackson said take-up had been in line with its forecasts which prompted it to purchase 30,000 tests. The total cost of the scheme is expected to be between £316,000 and £365,000.
'Feedback has been really positive,' he said. 'It means people can continue to visit vulnerable friends and relatives without worrying about whether they're infected or about how they will afford tests.
'People want to be responsible and help reduce the spread of Covid and we've stepped up where the government has not.'
Tests can be collected from 10 sites across the city: Alderman Lacey Library, Beddow Library, Carnegie Library, Charles Dickens Activity Centre, Cosham Community Centre, North End Library, Paulsgrove Community Centre, Southsea Library, Portsmouth Civic Offices and Somerstown Central.
Cllr Vernon-Jackson said the most popular collection point was Southsea Library where more than a quarter of all the tests had been distributed.