The latest forecast for the year ahead is higher than the growth figure of 1.7% predicted in October last year.
The Economic Commentary from the University of Strathclyde's Fraser of Allander Institute, sponsored by PwC, also estimates the economy will grow by 2.3% in 2015.
Although the forecast suggests a stronger economic recovery, researchers have also warned that weaknesses in both the Scottish and UK economies could still threaten future growth.
The Institute said the forecasts reflect higher than expected household spending, a pick-up on investment, improving trade conditions and increasingly optimistic business surveys.
Researchers said that in order to sustain growth over the long term, an increase in investment and net exports, as well as manufacturing and construction activity is needed.
More full-time jobs must also be created.
Brian Ashcroft, Emeritus professor of economics at the University of Strathclyde, said: "After six years since the start of the great recession we are now witnessing a stronger recovery, although this one is weaker than almost all previous recoveries.
"While there is room for considerable optimism, the continuing imbalances in both the Scottish and UK economies means the future path of the recovery is by no means certain."
He added: "In the light of continuing weak investment and rising UK regional inequality in growth and income per head, the Chancellor should use his forthcoming Budget to introduce a programme of private sector investment incentives, such as accelerated depreciation, with differential regional incentives, to reflect specific regional challenges.
"Academic evidence on the impact of regional policy in the 1960s shows that it works best when the national economy is recovering and firms are thinking about investing. So now would be the right time. "
Paul Brewer, senior office partner at PwC in Edinburgh, said: "We'd like to see this week's UK Budget focus on stimulating both domestic and inward investment.
"This is the right time for the Scottish Government to step up the pace here too, sustaining its own investment programme, making the most of EU investment support and by supporting our cities develop as great places to invest and do business by investing in their infrastructure and business locations."
The commentary found the financial services sector in particular has "enjoyed a sustained recovery since the fourth quarter 2012".
It added: "However, we note that there is a strong likelihood following the structural change that occurred after the great recession that some of this lost output may never return.
"This could still be the case despite the recent recovery in financial services. Moreover, with the recent RBS announcement that significant further cut backs in activity and job losses in the bank are to be expected the recent recovery in the sector might not be sustained."
Finance Secretary John Swinney said: "The Scottish Government welcomes the latest independent output forecasts for 2013, 2014 and 2015 from the Fraser of Allander Institute, which project higher growth than previous forecasts.
"This reflects the continued quarterly growth in the Scottish economy over the past six quarters to Q3 2013, with the Fraser of Allander Institute commenting that there is now little doubt that six years after the start of the recession we are witnessing a stronger recovery.
"The Institute also revised down its unemployment rate forecasts for 2013 to 2015.
"These forecasts follow on from recent GDP and labour market statistics, which showed the largest annual increase in employment levels since April-June 2007, and the economy continuing to grow.
"Scotland is a wealthy country and with the powers of independence we would be able to take further steps to secure a strong and sustainable recovery that supports key Scottish industries and boosts jobs and productivity."