Vowles has been instrumental at Brackley, initially with Brawn when he oversaw the race strategy that led to Jenson Button winning the 2009 drivers' title and the team claiming the constructors' crown.
After Brawn transitioned into Mercedes the following year, Vowles fulfilled a similar brief and has been credited with helping the team and Lewis Hamilton, in particular, to their various successes.
But Vowles has now been released from his Mercedes contract to join Williams, who were without a team principal after chief executive Jost Capito stepped down from his dual role in December.
"I cannot wait to start with Williams Racing," said Vowles. "It's an honour to join a team with such an incredibly rich heritage. The team is an icon of our sport, one I greatly respect, and I am very much looking forward to the challenge.
"Mercedes have been hugely supportive on my journey, and we part on excellent terms after over 20 years of working in Brackley. I am grateful for everything (team principal and CEO) Toto (Wolff) and the team have provided.
"It has been such a special experience to journey together through failure and success. Williams Racing have placed their faith and trust in me, and I will do the same in return.
"Williams has tremendous potential, and our journey together starts in a matter of weeks."
Williams will be hoping the 43-year-old's arrival marks a sea change in their fortunes, having finished bottom of the constructors' championship in four of the last five years.
Vowles will join the team on February 20, three days before the start of pre-season testing in Bahrain, which stages the first grand prix of the campaign on March 5.
Matthew Savage, chair of Dorilton which owns Williams, said: "We are delighted to welcome James to Williams Racing. He is one of the most highly respected talents in Formula One and will bring performance.
"He has been a key part of some of the most impressive feats in the sport over the past 15 years.
"As we continue our relentless pursuit for results, we believe that the appointment of James reinforces our dedication to ensuring we have energetic, experienced, and strong leadership."
Wolff paid tribute to his outgoing chief strategist.
"James has been a highly valued member of our team in his role as motorsport strategy director, playing an integral part in our success in recent years," said Wolff.
"Having worked with him since I first joined the team in 2013, I know how diligent, capable and talented he is and have taken great satisfaction from watching James develop and grow over the past decade.
"While we are naturally sad to be saying goodbye to such a capable member of the team, I have no doubts whatsoever that he has all the necessary skills to become a fantastic team principal in Formula One."