A team statement said the decision was made prior to the 2013 season, but its announcement had been postponed after the death of Claire's mother Ginny.
Claire Williams began in a media role at the team in 2002, before becoming director of marketing and communications three years ago. She will retain that position alongside her new title.
Frank Williams underlined that he sees Claire's new role as part of a succession plan.
"Over the past decade Claire has worked tirelessly for Williams," he said.
"Her knowledge of the sport and passion for the team is unquestionable and I'm proud to say that during her time here she has proven herself to be one of our most valuable assets.
"With Claire being appointed deputy team principal, I know the future of Williams is in extremely safe hands."
Claire Williams added that she was determined to bring Williams back to the forefront in F1.
"I have grown up in the sport and have learnt the ropes from one of Formula 1's legendary team principals and as a result I feel well equipped for this new challenge," she said.
"I understand the commitment that every person within the team gives each day to see our car out on the track and I am determined to see us back at the top."
Williams has undergone several management shake-ups in recent months.
Chairman Adam Parr departed in early 2012, while executive director Toto Wolff relinquished his role in January to take the helm at Mercedes.
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