The Hammers leave their 35,000-seater Upton Park venue at the end of this campaign to set up home at the remodelled London 2012 Games arena that will have a capacity of around 54,000.
"The opportunity this represents for West Ham is huge," Brady told Sky Sports News television.
"There are five times as many people on the priority list as there are available season tickets. All of the corporate hospitality facilities have already sold out. Every seat will be sold for every match."
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Excitement over the Olympic Stadium move is also having an impact on the pitch.
West Ham are eighth this season under impressive new coach Slaven Bilic, one point off the top six ahead of Saturday's home match with seventh-placed Liverpool.
"From our point of view, using the stadium and our brand to attract new players is incredibly important," Brady said.
"Lots of our players have attracted attention from other Premier League clubs but none of them have chosen to leave because they want to be part of the journey that we are on and that makes it feel very special at the minute."
The deal to allow West Ham to play home matches at the Olympic Stadium has drawn criticism from some who argue the Londoners will have an unfair advantage given the relatively low cost of being a tenant.
They will also raise money from the sale of Upton Park to property developers.
(Writing by Mark Meadows; Editing by Tony Jimenez)
