The death of his wife Virginia Williams led the team to postpone the announcement while was originally going to be made at the start of the season.
Claire Williams joined the team’s board in April last year and will continue her role as commercial director.
Frank Williams said he believes “the future of Williams is in extremely safe hands” following her appointment.
“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?óÔé¼Ôäóm proud to say that during her time here she has proven herself to be one of our most valuable assets.”
“This appointment also had Ginny?óÔé¼Ôäós blessing who I know would have been incredibly proud to have seen Claire taking on this position by my side,” he added.
Claire Williams said: “I have grown up in the sport and have learnt the ropes from one of Formula One?óÔé¼Ôäós legendary team principals and as a result I feel well equipped for this new challenge.”
“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.”
“It has been a sad month for my family and Williams as a company following the death of my mother, but as the season takes hold we must look to the future,” she added.
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Image ?é?® Williams/LAT