The First Minister said the mandatory vaccine passport scheme would end next week. However, Scots will still be asked to self-isolate if they test positive.
Business leaders welcomed the news, but warned “the hard work to get local economies moving needs to start now”.
Face coverings will still be strongly recommended in indoor public places and on public transport.
Ms Sturgeon announced the changes on Tuesday as she published a new strategic framework with the desire for a “sustainable return to a normal way of life” at its heart.
She said Scotland was “determined to retain a robust testing system” despite uncertainty over future funding and “frustration” with the UK Government.
It comes after Prime Minister Boris Johnson confirmed all Covid restrictions will end in England this week, including the legal requirement to isolate, and free mass testing will stop from April 1.
Speaking in Holyrood, Ms Sturgeon said restrictions were no longer necessary or justifiable.
"The strategic framework therefore makes clear that in future we will rely less on legally imposed measures to control the virus – and more on vaccines, treatments, and sensible adaptations and good public health behaviours,” she said.
The mandatory vaccine passport scheme will come to an end on Monday, while the legal requirement to wear face coverings in certain indoor settings and public transport is due to become guidance from March 21.
Ms Sturgeon added: “However, we will continue to strongly recommend the wearing of face coverings in shops and other indoor public places, and on public transport.”
Legal requirements on businesses and places of worship will also end on March 21.
The app for the passport scheme will remain operational, allowing businesses to use it on a “voluntary basis to reassure customers”.
Ms Sturgeon said testing would continue to be a vital part of Covid management, but indicated there would be a move away from “mass, population wide, asymptomatic testing, towards a more targeted system focused on specific priorities”.
She said a detailed plan for the future of the test and protect scheme would be outlined next month.
The First Minister said: “The only immediate change we are making to current arrangements on lateral flow tests for the general population is in our advice on the frequency of testing.
“Instead of advice to test before going anywhere to mix with others, we will from Monday revert to advice to test at least twice a week and in particular if you are going to a crowded place or mixing with someone who is clinically vulnerable.
“Lateral flow tests will remain free of charge in the transition phase.
"Indeed, we consider it important – in line with the principle of healthcare free at the point of use – that they should remain free of charge for any circumstance in which government recommends testing.
“This is a principle we will seek to uphold in our longer-term plan.”
Ms Sturgeon added: "I also want to emphasise that in Scotland, for now, we will continue to ask those who test positive for Covid to isolate for the recommended period.
"And we will continue to make self isolation support payments available to those who are eligible.
"We will, of course, keep the recommended period of isolation under review.”
The First Minister voiced her “frustration” over the impact of decisions in England on the resources available in Scotland for testing.
She said: “As of now, we have no clarity on how much of the Covid testing infrastructure the UK Government intends to retain; no clarity on how much investment will support it in future; and no clarity on whether the Treasury will provide additional resources to pay for it or demand instead that funding is taken from elsewhere in the health budget.”
She said dismantling the testing infrastructure in any significant way “would be inexcusable negligence given the threats that Covid still presents to us”.
The new Covid framework sets out a broad system based on low, medium and high levels of threat. Under the latter, people could be advised to limit social contacts and work from home, with “some temporary protections for high risk settings” reintroduced.
Colin Wilkinson, managing director of the Scottish Licensed Trade Association, said calling a halt to Covid passports “is common sense and fantastic news for hospitality businesses, particularly the late-night sector where restrictions over the last two years have had such a severe impact”.
He said: “However, the legal requirement to wear a face covering in indoor hospitality and other settings for another month is not the news we wanted to hear today from the First Minister at a time when our sector needs more positivity and confidence – confidence that will encourage customers to start getting out and about again.
“We are also way behind the rest of the UK in the process and that throws out confusing messaging to visitors to Scotland from south of the Border – visitors who will support our hospitality businesses.”
Mr Wilkinson also expressed concern over the Scottish Government’s advice to adopt “hybrid” working patterns.
Andrew McRae, policy chair of the Federation of Small Businesses in Scotland, said: “The lifting of the remaining Covid rules will be a weight off the shoulders of Scotland’s small business community.
“While the First Minister outlined her Government’s continued caution, she also spelled out a desire to return to a more normal way of life. That ambition to get back to business is something that Scotland’s local and independent firms share.
“However, the hard work to get local economies moving needs to start now. Ministers need to inject confidence as well as roll-out vaccines.”
A spokeswoman for the Night Time Industries Association Scotland said: “While we welcome the news that remaining restrictions such as Covid passports and the legal requirement to wear face masks will be dropped in coming weeks, the economic harm inflicted on the late night economy by 24 months of disproportionate restrictions will take years to recover from.
“We must now be given the opportunity to trade consistently and viably for the long term if businesses are to survive, and the Scottish Government must now focus on generating a sustainable recovery.”
The latest daily figures showed Scotland had recorded 6,427 new cases of the virus, as well as 18 more deaths within 28 days of a positive test.
Meanwhile 1,060 people are in hospital, Ms Sturgeon said, with 25 people in intensive care.
Scottish Conservative leader Douglas Ross welcomed the move away from “blanket legal restrictions towards an approach based on public health guidance”.
He said: “The demise of the discredited vaccine passport scheme is particularly welcome – and long overdue. There was never any evidence that the policy worked, yet it led to huge expense and inconvenience for businesses.
“In her statement the First Minister said her Government is moving to a system of representative sampling, away from mass testing. Yet she has chosen to create a fight with the UK Government over this issue, just weeks before she plans to scale back testing anyway.”
Scottish Labour deputy leader Jackie Baillie urged the First Minister to commit to the ongoing funding of testing as well as contact tracing “to protect the people of Scotland”.