The announcement comes as the First Minister unveiled her new programme for government, which sets out how the country will be run for the next 12 months.
More than 130,000 cans and plastic bottles are binned in Scotland each day, many of which end up as litter.
Plastic pollution is harmful to the environment and to wildlife.
Studies show millions of marine creatures and seabirds die every year as a result of entanglement or eating man-made debris after mistaking it for food.
Research suggests such a scheme could stop 18 million cans and 21 million bottles from ending up in landfill and beaches in Scotland each year.
The design for Scotland’s new system has yet to be finalised, but will likely involve an extra cost being levied on the purchase price of a packaged drink, which is then refunded when the container is returned to a collection point ready for recycling.
A recent poll shows nearly three quarters of Scots support the move.
The schemes have been proven to improve recycling rates for drinks containers elsewhere.
The current rate stands at 50 per cent in Scotland, but rates in places such as Norway are as high as 95 per cent.
Environmentalists believe a 90 per cent rate could be achieved here within two years.
Campaigners have welcomed the announcement.
Gina Hanrahan, acting head of policy at WWF Scotland, said: “We already know that deposit return schemes for bottles work in other countries and would be popular with people in Scotland.
“If everyone used as many resources as we currently do, we’d need three planets to survive. Reducing, reusing and recycling is essential if we’re to limit our use of precious resources to sustainable levels.”
Willie Mackenzie, oceans expert at Greenpeace UK, added: “Governments are waking up to the frightening scale of ocean plastic pollution and it’s brilliant to see Scotland leading the way in helping to tackle it.
“On Greenpeace’s recent research expedition around remote Scottish coastlines, plastic bottles and packaging were simply everywhere.
“A staggering 16 million plastic bottles end up in the environment every day in the UK, and deposit return schemes are a great way to make sure more of them are collected and reused.
“Today’s announcement by the First Minister is a massive step in stopping plastic pollution, and the result of tireless campaigning by many groups and individuals.
“With businesses and an overwhelming majority of the public in favour of deposit schemes, the Scottish Government now has a mandate to implement as robust a system as possible to help reduce plastic pollution. Hopefully it won’t be too long before the rest of the UK follows suit.”
Zero Waste Scotland has been charged with designing the new system.
Chief executive Iain Gulland said: “By attaching a value to things we think of as waste, a deposit return scheme follows on from the hugely successful carrier bag charge, and will help reduce litter as well as increasing recycling.”
The latest programme for government, which also sets out a plan to phase out petrol and diesel cars by 2032, introduce low-emission zones in Scotland’s four major cities and potentially put a levy on disposable coffee cups, has been hailed as “the greenest” in the history of the Scottish Parliament”.
Friends of the Earth Scotland director Dr Richard Dixon said: “The Scottish Government has put improving and protecting the environment at the heart of their legislative and policy programme.
“Promises here will reduce climate change emissions, save people from air pollution and help Scotland become a leading example of a low-carbon country.
“This package is a very significant step towards a fossil-free Scotland.”
Presenting the plans, Nicola Sturgeon said: “To succeed, Scotland must lead change, not trail in its wake.
“We must aspire to be the inventor and the manufacturer of the digital, high tech and low carbon innovations that will shape the future, not just a consumer of them.
“To encourage others to see Scotland as the place to research, design and manufacture their innovations - for us to become a laboratory for the rest of the world in the digital and low carbon technologies we want to champion - we must also become early adopters of them.
“We must be bold in our ambitions.”