The findings also estimate that Scotland, staying part of the UK, is in line for "relatively slow" employment growth in the same period.
The Scottish Government last night seized on the figures and described them as proof of the Union providing a "bleak" future.
The economy is shaping up to be the key battleground in the debate on whether Scotland should become independent, or stay in the Union.
Polls have consistently shown the Yes side behind when respondents are asked about the country's economy under independence.
Last week's publication of the so-called GERS report, effectively Scotland's balance sheet, offered more mixed news for the independence campaign.
It revealed Scotland's deficit had risen to 8.3% of economic output in 2012-13, compared with 7.3% for the UK as a whole.
The larger deficit was caused by a sharp dip in oil revenues, which the SNP has made a key plank of the case for independence.
However, a new report by the UK Commission for Employment and Skills (UKCES) has shed a different light on Scotland's long-term economic prospects.
The UKCES is a quango and "social partnership" that includes senior business people and trade unionists.
It has produced a series of labour market reports under the "Working Futures" banner, which include projections on employment and growth.
The latest report provided a range of forecasts for the UK between 2012 to 2022, including for Gross Value Added (GVA). In layman's terms, GVA is the output of all industries in an economy.
The report also included a referendum section, namely, that the authors worked on the assumption that the "UK will continue to include Scotland".
However, the Sunday Herald has obtained a leak of an unpublished annexe of the report that supplied a country-by-country breakdown.
The GVA figure for England is an annual average of 1.9% over 10 years, 1.7% for Wales and Northern Ireland, and Scotland bottom of the league at 1.6%.
The Scotland figure is also lower than the estimated UK-wide average of 1.9%
In the previous period - 2002-2012 - Scotland was ahead of Wales and closer to the average rate of growth in England.
The annexe noted: "Scotland and Northern Ireland experienced average growth rates similar to England during 2002 to 2012 but a much weaker recovery of growth is projected between 2012 and 2022."
The "key messages" section of the annexe stated that the southern parts of England will "continue to experience the most favourable trends", while the rest of England and the other UK nations will "fall further behind" relatively.
The sectoral breakdown is also mixed, with Scotland behind the UK growth average in four of six areas: the primary sector and utilities; construction; trade, accommodation and transport; and non market services.
Scotland has the same projection for "business and other services" and exceeds the UK average on manufacturing.
On employment growth, the annexe projected Scotland as being ahead of Wales over the 10-year period, but behind the UK as a whole.
A Scottish Government spokesman said: "This report, from some of the most senior business and trade union leaders in the UK, admits that the future within the union is bleak.
"Lower long-term growth than the UK and poorer long-term employment prospects is the reality this UK report reveals.
"Scotland is the 14th richest country in the OECD. Only with control of our own affairs, only with the powers of independence, can deliver the just and prosperous nation we all want to see. Without full powers in Scotland jobs and growth are under threat.
"That's what is at stake in September's vote."
A spokesman for Better Together said: "While we cannot comment on figures that haven't been released yet, it is absolutely the fact that Scotland is one of the highest performing parts of the UK.
"Unfortunately, any published figures these days allow the SNP to indulge in their favourite game of UK-bashing.
"To the Nationalists, unemployment dropping is a reason to leave the UK and unemployment rising is also justification for separation.
"Good economic figures are a sign that we should go it alone, as are bad ones. Anything and everything is used to justify their one, faltering policy."
A UKCES spokeswoman said the annexes would be published soon and declined to comment on the independence claims.