The Resolution Foundation think-tank found the financial downturn in 2008 and the subsequent recovery have been felt "very differently" across the UK.
Scots have experienced the largest percentage growth in income, up 4%, while incomes in Northern Ireland (-2.4%), the West Midlands (-1.9%) and eastern England (-0.8%) were still below pre-crash levels.
But it warned the pace of the recovery in living standards across the UK is set to slow over the next four years, with many poorer households losing out altogether.
The data is contained in the Resolution Foundation's annual audit of living standards, which looks at the detailed picture around the UK.
Overall, it found typical household living standards have finally surpassed their previous peak levels.
Typical household income now stands at £24,300 - above the 2009 high - against a backdrop of rising employment and low inflation.
The independent report, entitled Living Standards 2016, looked at the path to recovery from the 2008 crash to last year.
It noted: "Taking three-year averages... median incomes before housing costs increased by 4% in Scotland and by 2.9% in London between 2008 and 2015, but fell by 2.4% in Northern Ireland and by 1.9% in the West Midlands."
When housing costs were taken into account, Scotland again came out on top, with growth of 6.6% in the post-crisis period.
However, employment was found to have been "essentially flat" in Scotland, rising 0.4% from May 2008 to November 2015.
And the foundation's outlook for living standards across the UK suggests the strong broad-based recovery of recent years may not last.
It warned that rising inflation, reductions in welfare and an uncertain outlook for pay could lead to a slowdown in household income growth, with living standards for typical households rising by an average of just 1% a year over the lifetime of the current UK parliament.
The think-tank also cautioned that while the downturn and recovery have been marked by falling income inequality, that pattern is likely to be reversed in the coming years.
Its forecast suggests real incomes for the poorest quarter of households are set to fall over the parliament, due largely to the impact of the four-year benefit freeze and cuts to Universal Credit, despite the introduction of the national living wage.
Matthew Whittaker, chief economist at the foundation, said: "The financial crisis led to one of the longest and deepest squeezes on household incomes in living memory.
"But the welcome recent backdrop of strong employment growth and ultra-low inflation has meant that typical household incomes have finally surpassed their previous peak.
"It's particularly encouraging to see that the recent recovery has been broadly shared, with low-income households receiving the strongest living standards boost of all.
"But there are huge uncertainties surrounding the future path of living standards. The pace of recovery is likely to slow over the remainder of the parliament. Substantial benefit cuts will bear down most heavily on poorer households, with many seeing their incomes fall as a result."
A Scottish Government spokesman said: "Scotland's economy has recovered strongly from the downturn in 2008 and continues to grow.
"We remain focused on continuing to improve Scotland's performance in the priority areas of investment, innovation, inclusive growth and internationalisation set out in Scotland's economic strategy, and we will continue to use every power at our disposal to build on this growth and realise the full productive potential of Scotland."