Mountford announced that she would be leaving the show towards the end of this year's run and Brady, Martha Lane Fox and Michelle Mone had been tipped to take over the role.
Brady will feature alongside Sugar's other aide, public relations executive Nick Hewer.
She said: "I am thrilled to be involved, having worked with Alan for 16 years. It's great to extend our relationship to the programme."
The 40-year-old managing director of Birmingham City has appeared on past series of The Apprentice in the interview phases, and also led the women's team to victory in 2007's Comic Relief Does The Apprentice.