Mayor of London Boris Johnson revealed the news on Wednesday following a meeting of the LDDC as the Hammers took a huge step towards becoming the first tenants of the East London venue.
Contractual matters still need to be resolved before the deal is confirmed, but Brady is already looking forward to the proposed relocation and the opportunities it could open up.
She said in The Sun: "If I had to sum up how I feel, it would be excited. Excited at the prospects for the club, our supporters and East London.
"I'm looking forward to working with our local partners to target groups in need of employment. I am excited at the prospect of growing our business.
"I am excited at the chance to work with our supporters to make this a stadium that befits their proud history and that they can call home. The opportunity for our club to really compete at the highest level and grow to fit its fanbase is immense."
Brady added: "I have talked a lot about our plans and meant every one of the promises I made on behalf of West Ham. What excites me the most is that I finally believe that the time has come to start putting those plans into action and delivering on those promises. And that is what it has always been about for me."
West Ham have been targeting the stadium for the past three years but Brady expects the hard work to really start once final negotiations have been completed.
She added: "Of course, we have only been named highest-ranked bidder and we still have to see the ball over the line in the final negotiations.
"Then the hard work can really start to create a stunning new home.
"Yesterday was a fantastic day for West Ham United, but I think there are even better times ahead."
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