The move means pubs, restaurants and cafes can open for food and non-alcoholic drinks, subject to a 6pm curfew, while non-essential shops can open their doors from 6am on Friday.
But the first minister was accused of dealing a “hammer blow” to businesses in capital Edinburgh, after keeping the city in the second-toughest level 3 despite low numbers of coronavirus cases.
Also moving down from level 4 to level 3 of the Scottish Government’s regional restriction system are Stirling, East and South Ayrshire, East and West Dunbartonshire, Renfrewshire, East Renfrewshire, North and South Lanarkshire and West Lothian.
Ms Sturgeon told the Scottish Parliament it had been decided not to move Edinburgh down from level 3 to 2 - which would have allowed hospitality venues to stay open indoors until 8pm and serve alcohol outside until 10.30pm - because of fears of driving up transmission in the run-up to Christmas following an uptick in cases in recent days.
“A move to level 2 in Edinburgh would mean opening up significantly more services in our second biggest city in the two weeks before Christmas,” she said. "That move would carry significant risk of increased transmission.
“We want as much assurance as possible that the situation is as stable as possible before making that move. For that reason - and this has been a difficult decision - we have decided not to move it over to level 2 this week but we will consider this again next week.”
“Edinburgh went into a ‘16 day’ targeted lockdown on October 9. We are now at day 60 with no logical explanation of how and when Edinburgh moves to a lower tier.
Edinburgh South’s Labour MP Ian Murray said: “The announcement that the capital will remain at tier three, despite widely trailing a move to tier two, is a hammer blow for businesses and jobs at the most important time of the year.
“This is compounded by the SNP Government’s failure to offer adequate support for employers, even though up to £1billion in funding it has received from the UK Government remains unallocated."
Ms Sturgeon said that coronavirus cases had fallen “significantly” in all 11 of the west and central Scottish areas placed in level 4 last month, with numbers of positive tests falling in Glasgow from 281 per 100,000 population in the week of 13 November to 150 in the week of 4 December.
She said the Scottish government was responding with a “proportionate but still cautious” relaxation of restrictions.
Ms Sturgeon said Scots should “allow ourselves a smile” as the first vaccinations against Covid-19 took place north of the border on Tuesday.
“This is a milestone we have all longed for,” she said. “It offers hope, at long last, that we may now be at the beginning of the end of this pandemic.
“I want to thank everyone involved, now and in the months ahead, in delivering what will be the biggest vaccination programme in our history.
“Today we should all allow ourselves a smile.
“But we must not drop our guard.”
Five other council areas in Scotland will see restrictions eased.
Inverclyde, Falkirk and Angus will move from level 3 to level 2 and Dumfries and Galloway and the Borders will move to level 1.
Moving to level 2 also allows cinemas and bingo halls to open, and permits outdoor sports, while in level 1 up to six people from different households can meet inside a home.
Scotland recorded 692 positive Covid tests on Monday and 33 fatalities, bringing its total official death toll to 3,950. Some 983 people are in hospital in Scotland, with 57 in intensive care.
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