The living bridge design, drawn up by Thomas Heatherwick who designed the Cauldron for the London Olympics, will be put in for planning next year.
Arup will work up the structural designs ahead of lodging the plans for the bridge which will link Covent Garden to the South Bank.
The future of the project will hinge on whether a private backer can be found to finance the bridge as the GLA has said no public cash will be available for the project.