Avery will continue to be based in London. He will remain in charge of Arena and retain the role of UK managing director of Havas Media Group.
Avery said: "There has never been a better time to work with the world’s top brands to reach global audiences through sport and entertainment because digital technology means we have so many more opportunities at scale.
"Havas Sports & Entertainment already has a world-class team of more than 600 people who have a track record of delivering innovative, high-quality solutions to our clients."
HSE’s clients include Adidas, Barclays, Coca-Cola, EDF and Chelsea Football Club.
Avery will become one of the most senior Britons in the French ad group, which is run by Yannick Bolloré and controlled by his family’s Bolloré Group.
Boyer’s move to Vivendi is likely to be amicable because Vincent Bolloré, the father of Yannick Bolloré, chairs the entertainment giant, which owns Universal Music, the world’s biggest music company, and Canal+, the pay-TV company.
Vincent Bolloré has been pushing for Vivendi and Havas, the world’s sixth-biggest ad group, to work more closely together on advertising and content partnerships.
Yannick Bolloré, the chief executive of Havas, said: "Pedro and his team will work alongside myself and the executive committee to foster a better integration of Havas Sports & Entertainment within the group while designing the future of our offering and strengthening our global leadership position in the world of content, entertainment and sports."