The index, which is compiled using data from over 10,000 employers, shows there were 8% more opportunities on offer in May than in April.
There were more opportunities for jobseekers in over 90% of the UK's employment sectors last month compared with April, with one in four making over 10% more jobs available, the index found.
It also showed on an annual basis the average growth in opportunities for every sector of UK employment stands at 21%, with only three sectors (accountancy, financial services and purchasing), less healthy now than they were in 2012.
Among the sectors enjoying the most notable growth were the education and health and medicine professions, both experiencing annual growth of around 60%. The training sector proved the biggest monthly riser, up by 26% compared with April.
Despite the optimistic outlook for job opportunities, the Index revealed salary growth remained flat last month. This means remuneration is at the same level it was this time last year.
James Reed, chairman of Reed, said: "In line with the season, the jobs market has bloomed this spring after steadying in April. We are particularly encouraged by the fact that the majority of employment sectors are showing growth.
"We believe that a jobs-led recovery is the way forward for the UK economy and, with the latest service sector and house price data starting to indicate the wider health of the economy picking up of late, we are starting to see the tentative recovery very much being led by the buoyant jobs market."
Reed said: "Looking ahead, it will be interesting to see whether this month's GDP and ONS figures follow suit. Both measures have recently shown encouraging, if modest growth and there are strong signs the growing health of the jobs market will continue to help drive the economy forward."