Output and new orders in May also rose at their fastest levels since the Royal Bank of Scotland (RBS) monthly PMI report began in 1988.
However, both costs and output prices also showed steep rises as inflationary pressures increased.
The seasonally adjusted headline business activity index – a measure of combined manufacturing and service sector output – posted 61.5 in May, up from 55.4 in April. Sharp expansions were recorded across both the manufacturing and service sectors
New business increased at an unprecedented pace and companies scaled up employment to an extent previously unseen in the survey's history.
Although Scotland saw strong growth in new orders, it was the second-slowest of the 12 UK regions covered.
Business confidence in Scotland also improved to a new record high but remained just below the UK average. However, the rate of job creation in Scotland was slightly stronger than the UK average.
Input costs continued to rise sharply during May, with the rate of inflation quickening to the fastest for a decade. Panellists reported higher costs for a range of raw materials, as well as increased shipping charges. Rising staff costs were also mentioned at a number of companies surveyed.
Malcolm Buchanan, chair of RBS’s Scotland board, said: "Growth in the Scottish private sector hit unprecedented levels in May amid a further loosening of lockdown restrictions and strong confidence in the year-ahead outlook."