The initial plans are now subject to the approval by the Mayor of London are for a temporary facility to be operational before the end of the year.
They plan to be used by the club’s first and B teams for the next five years.
Brentford’s long-term vision includes plans for a permanent, state-of-the-art performance centre on the site.
A club statement read: "This decision means that the club can replace the existing buildings at Jersey Road. The new training facility, whilst temporary, will be of a much higher standard and represent a significant improvement on what we have now.
"It will act as a stepping-stone towards our longer-term vision for a state-of-the-art performance centre."
The announcement follows a consultation process with the local community, and preliminary works are now underway.
Additional reporting from Reuters