Dawson starts on Monday after leaving Southern Water in July after six years at the utility giant.
A spokesperson for Murphy said: “With over 30 years of infrastructure experience we are confident that Les will make asignificant contribution to the continued growth and future success of the Company, and we look forward to working closely with him.
“The appointment will support the management team’s focus on securing and increasing our core business, whilst at the same time developing new opportunities.”
Murphy was established in the 1950s by industry legend John Murphy who died last year at the age of 95.
The company has a turnover of £420m and is still owned and managed by the Murphy family.