Aberdeen, Fife, Dumfries and Galloway, Moray, Shetland and the Western Isles regions will all see their school pupils return as of Monday, 12 April.
Social distancing measures will be more relaxed in the school grounds, but pupils will still need to wear face coverings.
In most local authority areas, the Easter holidays are not due to end until April 19 which is when the majority of Scotland's pupils are due to return to school.
Pupils in Edinburgh and Midlothian councils however will return to school a day later on 20 April.
Scotland’s primary school pupils had already returned to in-class teaching before the Easter break but a part time blended-learning system had been in place for secondary pupils during the phased return.
Pupils in the shielding category are the only exception to pupils returning over the next week. First Minister Nicola Sturgeon said that pupils who have been shielding during the pandemic should stay at home until 26 April, in line with advice from the chief medical officer.
Ministers confirmed there will be twice-weekly lateral flow testing for all school staff in primary, secondary and special schools, and for all secondary school pupils in years four, five and six.
Mr Swinney has previously said it was likely that adults in schools would still have to stay at least two metres away for each other, and from pupils, and that a “whole variety of other mitigation measures” would also be in place to prevent virus spread.