He had earlier accepted the resignation letter of then premier Ted Baillieu.
In a brief speech Dr Napthine said he looked forward to the opportunity.
"It's an honour and a privilege to be sworn in as premier of Victoria," he said.
He also paid tribute to Mr Baillieu.
"I'd like to particularly acknowledge the former premier, Ted. Ted, I count as a true friend.
"He's been a terrific servant of Victoria.
"I know this task has enormous responsibility and enormous challenges and I will do my level best to respond positively to those challenges and opportunities and will work hard for the people of Victoria."
Dr Napthine's portfolios now include arts, ports, major projects, regional cities and racing.