The Royal Borough's decision to scrap the raised walkway has been backed by central government.
The bridge was part of the original planning permission for the 448 home estate in Blackamoor Lane.
But following a public outcry at news of the plans, the council said the condition should be relaxed as the structure would be detrimental to the moor.
This week Secretary of State for communities and local government Eric Pickles said he will not be calling the decision in for consideration.
Instead of building the bridge, developer Shanly Homes will have to prepare and fund a flood evacuation plan for the estate and provide £150,000 of developers contributions towards the enhancement of York Stream.
Cllr Christine Bateson, cabinet member for planning and partnerships, said: "This is really good news for local residents who really did not want to see such intrusive structures blighting the open and uncluttered nature of their popular local open space."
Top Ten Articles
CCTV images have been released of men police would like to speak to in connection with a homophobic attack on a couple as they took a train home from a Valentine's Day meal.