Jack Sullivan, 22, was managing director of West Ham’s women’s team until he stepped back from the role in May.
It is unclear what role or how much influence he and his brother will hold on the board.
Daniel Cunningham, the son-in-law of co-owner David Gold, has also been added to the list of directors.
The appointments are part of a reshuffle at board level after Czech billionaire Daniel Kretinsky last week bought a 27 per cent stake in West Ham in a deal worth more than £180million.
Sullivan and Gold both sold shares to Kretinsky, who is now the second largest shareholder after Sullivan, who has 38.8 per cent.
Kretinsky and his colleague Pavel Horsky have also taken seats as directors of WH Holding Ltd, the holding company which controls West Ham, while other Czech partners, Peter Mitka and Marek Spurny, have also been appointed directors on the board.