Van Boxmeer will initially join the mobile phone giant as a non-executive director in July before taking over from current chairman Gerald Kleisterlee on November 3, 2020, Vodafone said.
Kleisterlee will retire from the board on that date having been Vodafone chairman for nine years.
Van Boxmeer has been Heineken's chief executive since 2005 but will step down next month.
In a statement, Nick Read, Vodafone’s chief executive commented: "I am delighted that Jean-Francois will be joining Vodafone and becoming Gerard's successor.
“He has presided over a highly successful period of transformation and value creation at Heineken, has extensive international experience in driving growth through both B2B and B2C business models, and is highly-regarded as one of the longest standing and most successful CEOs in Europe. I look forward to Jean-Francois playing a key role in the next stage of Vodafone's strategic development."
Van Boxmeer is also a member of the shareholders committee of Henkel and a non-executive director at US food giant Mondelez.
In other changes, Vodafone said David Thodey will replace Sir Crispin Davis on its Audit & Risk Committee after the next AGM, though Davis will remain a non-executive director of the FTSE 100-lised company.