Gary Davies, a 50-year-old from Greenwich, will appear at Bromley Magistrates’ Court on Monday.
The 56-year-old woman’s body was found in the back garden of a house in Tunnel Avenue on Saturday.
A post-mortem was carried out on Sunday and gave the cause of death as stab wounds to the back.
Detectives do not think the incident is domestic, but Davies and the woman are believed to have known each other.
Officers believe they know the identity of the victim and have informed her next of kin, but formal identification is yet to take place.
Anyone with information is asked to call detectives on 020 8721 4054.