Millican, the finance and regulation director, had been interim chief executive since the sudden death of Richard Ackroyd in autumn last year.
“I am honoured and delighted to take the helm at Scottish Water, leading a committed and passionate workforce delivering ever improving services to our customers,” Millican said.
“The service we provide is an essential one, and I know everyone in Scottish Water will continue to do the very best we can to deliver for our customers and communities across Scotland.”
The appointment had the unanimous support of the Scottish Water board and has been approved by ministers.