He will report directly to CEO Chase Carey as the organisation continues to evolve following the recent departure of erstwhile commercial chief Sean Bratches.
Pincus replaces Murray Barnett, who held the slightly different title of director of sponsorship and commercial partnerships, and who leaves the company this week.
Pincus has demonstrated his potential value to F1 over the past four years with his role with key partner Heineken International, a title sponsor of several races.
He joined the beer giant initially as sponsorship consultant in March 2016, becoming the head man for the F1 deal the following January, and then sponsorship director last year.
Prior to that, he held a variety of roles at advertising and marketing agencies, including a spell with Zak Brown's JMI organisation. As well as motor racing, he has been involved in sponsorship deals in football, tennis, golf and sailing.
"Having worked closely with him over the past three years I know he has the experience, expertise and leadership qualities to grow our business and continue to take F1 forward on its exciting journey," said Carey.
"Ben has an incredibly impressive network and knows the F1 world as well as anyone. He will hit the ground running and get the very best out of his team."
Carey also paid tribute to the departing Barnett: "I want to thank Murray for his hard work over the past three years in welcoming new partners to F1 and delivering the best for our existing partners.
"He joined us right at the start of our F1 journey in 2017 and has been a big part of the team that has transformed F1 into a leading global media and entertainment brand.
"He has built a focused and talented team that will continue to drive us forward as a business and I want to wish him well as he moves on to new challenges."