New analysis from the Office for National Statistics showed they came after six London boroughs, plus Milton Keynes and Berkshire.
The 2015 measure of Gross Value Added (GVA) showed Edinburgh growing at 4.5%, the fastest pace of any UK city other than Belfast.
GVA is a calculation of economic output similar to Gross Domestic Product.
However, neighbouring East Lothian and Midlothian were among those 10 local areas with the UK's lowest GVA, along with East and North Ayrshire.
While Aberdeen and Aberdeenshire, combined, had the 10th highest GVA in the UK, it had the third highest level of decline, after Central Bedfordshire and West Northamptonshire.
The north east economy declined 2.5% in the first full year of the downturn in the oil and gas sector.
The figures compare statistically comparable areas known as NUTS - Nomenclature of Units for Territorial Statistics.
GVA per head was at nearly £300,000 in the City of London, reflecting its measure of financial commuters' economic impact. The measure was just under £37,000 in Edinburgh and also in north east Scotland.
In East and North Ayrshire, as well as East Lothian and Midlothian, GVA per head in 2015 was just above £15,000.
Across the UK, GVA per head was calculated to have grown 2.1% during 2015, to £25,350.
At the level of nations and regions, Scotland was on £23,700, having grown 1.8% during the year.
Edinburgh and north east Scotland have been named among the top 10 most affluent parts of the United Kingdom.