The huge sum will come in the form of contracts for firms based north of the Border, in addition to increased tourism. According to the Bank of Scotland study, the benefits will last well beyond the end of the event next month.
The bank says thousands of people will share in the Olympics windfall, as money trickles down into different areas of the economy.
Despite initial criticism that much of the boost to the economy would be centred on south-east England, its analysis shows Scots firms are expected to share in a £774 million jackpot through construction contracts or to supply events. A further £185m is anticipated to come from Games-related tourism in Scotland this summer and over the next five years.
Tourism chiefs have already set plans in motion to capitalise on the increased exposure the event – which starts on July 27 – will bring to Scotland, thanks to the Olympic torch procession around the country last month and the international focus on the UK as a whole.
The report examined the overall impact of the Olympic and Paralympic Games, from when London secured the right to stage them in 2005 until 2017, when the "legacy" period is due to end.
Overall, Scotland will receive the fifth-highest economic boost outside of London, with the banks estimating that the Games are worth £16.5bn in GDP to the UK economy.
Gareth Oakley, head of Bank of Scotland Commercial, said: "London 2012 is the most important sporting event the UK has ever staged and Scotland is reaping the benefits.
"Delivering the Games has required an unprecedented level of capital investment over the past five years and the economic ripples of this are being felt across the UK.
"The economic impact to Scotland is a real boost, and the fact that businesses in the country have seized the opportunities presented by the Games and have delivered such a big contribution to GDP must be acknowledged."
Scottish firms have secured a number of contracts for Games-related work, and have been involved in building both the Olympic stadium and the Aquatics centre.
Suppliers from north of the Border have also enjoyed increased opportunities, both with the organising committee and as part of the supply chain.
The bank states the net spend on tourism in Scotland over the period will be split between £40m during the Games, with rest coming after 2012 through a legacy effect.
Hotels and restaurants will see the biggest impact, with up to 18% of the anticipated tourism-related business taking place in Scotland, while retail and transport will provide 4% and 12%, respectively.
Ramin Golzari, director at bagmakers Highlander (Scotland) Ltd, one of the firms to be awarded a contract, said he has doubled his turnover through contracts secured in relation to the Olympics.
He said: "We have just secured several new contracts worth over half-a-million pounds. Turnover increased by 20% last year and it will increase by a further 30% in this financial year. The impact of the Games is marked. As a snapshot of what this has meant to the company we just need to look at our sales figures for May – a 100% increase on the same month last year.
"We have taken on new staff to cope with the increase in business and doubled the size of our warehouse in the last year."