One woman, identified only as DSD, was the first of Worboys' victims to make a complaint to the Met in 2003 - although another woman had approached City of London Police the previous year - while the other, NBV, contacted them after she was attacked in July 2007.
Between 2002 and 2008, Worboys, who was jailed for life in 2009, carried out more than 100 rapes and sexual assaults using alcohol and drugs to stupefy his victims, said Mr Justice Green at London's High Court.
He ruled that the Met was liable to the women for failures in its investigation and that damages would now be assessed.
DSD and NBV brought their claims under Article 3 of the Human Rights Act.
DSD alleged that she suffered a depressive disorder as a result of her treatment by officers, while NBV claimed to have experienced anxiety, guilt and an exacerbation of post-traumatic disorder and depression.