- This story was corrected on 27 October - see final paragraph
The foundation said it would continue to operate as a distinctive entity and would retain all 43 of its staff.
Will Hutton, the former editor of The Observer and a government adviser on public sector pay, will continue as its vice-chair.
The foundation had been the subject of a winding-up petition filed in the High Court, citing a £26.9m pensions deficit that rendered it insolvent.
The charity said the acquisition minimised losses to creditors, including the 600 current and former staff in its pension scheme.
Members of the pension scheme are likely to lose about a sixth of the value of their pensions, according to estimates from FRP Advisory, the insolvency specialists who advised the foundation.
Stephen Bevan, managing director of the foundation, said: "There are many areas where our work and that of the university are very complementary.
"This alliance will help us consolidate our reputation for excellence in our analysis of labour market and employment trends and our ability to advise policymakers and organisations on how to meet the challenges of the future."
Professor Sue Cox, Dean of Lancaster University Management School, said: "This development cements a long-standing relationship between LUMS and the Work Foundation. There are obvious synergies – for example in the areas of HR, innovation, labour economics and organisational health and wellbeing – and we are very excited about combining our respective strengths."
- Members of the pension scheme are expected to lose a proportion of the value of their pensions. The statement that members would lose a sixth of the value of their pensions was the result of a misunderstanding. FRP Advisory, the insolvency specialists who advised the foundation, says it cannot estimate what losses pension scheme members will face.
The pension scheme is the largest of several unsecured creditors. Of a total estate of £4m, the scheme is likely to receive only around £3.5m, meaning it will be left with an approximate shortfall of £23.5m.