Murray's first focus will be on driving sales of the company's Cygnus software, which allows users to process data and manage databases and is used by agencies including Golley Slater and Tullo Marshall Warren.
He will also oversee new product launches from the company this year, reporting to managing director Tony Hayday.
Murray, who left Occam last July after four years, said: "For me, the move to The Software Bureau was a natural progression. When I first heard about the software, I was impressed by the potential autonomy and independence it provided for clients."
The Software Bureau was known as Information Equals Power until last summer.
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