The Bank of Scotland purchasing managers' index (PMI) for October increased to 52.7, up from the 52.2 recorded in September.
The October data also revealed that employment across the private sector increased, while the rate of job creation was moderate, it was up on the September figure.
Scottish private sector companies have continued to face rising input costs, with input price inflation rising sharply in October.
Output charges rose modestly, with the rate of output inflation remaining unchanged from September.
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Despite reports of higher raw material prices and wage bills, the higher labour costs have not deterred businesses from taking on more staff.
Fraser Sime, regional director of Bank of Scotland Commercial Banking, said: “Scottish private sector companies began Q4 positively, with output growth accelerating to a three-month high.
“The upturn was broad-based, with both manufacturing and service output expanding at quicker paces.
“Latest data also pointed to an overall expansion in new business orders, although growth was only evident in the service sector.
“Manufacturers received slightly fewer new business orders, albeit higher output allowed backlogs of work to clear.”
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