Brady had joined West Ham's board in 2010 after joint chairman David Sullivan and David Gold completed their takeover of the Premier League club.
Brady played an important role in West Ham's move from Upton Park, which had been the club's home ground for more than a hundred years, to the London Stadium in 2016, a deal that substantially increased matchday capacity for West Ham to around 60,000 seats.
"It has been a privilege to work alongside the Board, management, players, staff and supporters at West Ham United," Brady said in a statement.
"Together we have achieved remarkable milestones, but the highlight for me will always be lifting the UEFA Europa Conference League trophy - a moment that will stay with me forever," she added about the 2023 triumph.
Brady, despite commercial progress, became a polarising figure among West Ham supporters, with criticism of the transition from Upton Park to London Stadium, increased ticket prices and not capitalising on the club's Conference League triumph.
West Ham are currently in a relegation battle in the Premier League, sitting just two points above 18th place Tottenham.