The government is providing the cash following a “damning inspection” in May.
The report by Charlie Taylor, HM chief inspector of prisons, found it was severely overcrowded with 80% of men sharing cells designed for one person.
Mr Taylor made an immediate demand for improvements.
His report also described increasing violence, easy access to drugs, and rising rates of self-harm.
The prison population has risen from 1,364 in 2021 to over 1,500 inmates this year and it remains one of the most crowded prisons in the country.
Justice Secretary, Shabana Mahmood, said: “we are taking immediate action at HMP Wandsworth to do what is necessary to protect the public”.
