She collapsed and never regained consciousness. Traces of Midazolam were later found in her body.
Cobb, 38, from Yateley, Hampshire, was convicted on 17 May of the manslaughter of junior sister Susan Annis, 31.
The jury at the Old Bailey also found him guilty of four charges of drugging women with intent to rape, and guilty of two offences of rape at the casualty department at St Peter's Hospital, Chertsey, Surrey.
The prosecution told the court that Miss Annis, from Crawley Hospital, West Sussex, died when Cobb spiked her drink with the sedative Midazolam at a nurses' home at the Royal Brompton Hospital, west London, in November, 1996.
Heart stopped
The drug, which is used by casualty departments for minor surgery, can cause lack of consciousness and memory loss.
The court heard that Cobb's intention was to stupefy Miss Annis in order to rape her but she suffered an adverse reaction to the drug and her heart stopped.
She collapsed and never regained consciousness. Traces of Midazolam were later found in her body.
Cobb was arrested in January 1999 after a woman patient complained she blacked out on a trolley and came round to find herself being raped by a nurse.
She drifted in and out of consciousness but was later able to remember enough to raise the alarm.
Her blood was taken and found to contain Midazolam. She had not been prescribed any medication by the hospital.
After Cobb's arrest, it was found that his uniform had traces of Midazolam in the pockets. A syringe containing traces of a sleeping drug was found at his home.
More victims feared
Police fear Cobb is responsible for raping other women patients who may be unaware they have been attacked.
Detective Superintendent Dave Cook of Surrey Police said another woman patient had come forward during the trial after recognising Cobb's photograph in newspaper reports.
Mr Cook said: "If we had known about her before, Cobb would have been charged. Now it will be up to the Crown Prosecution Service."
Detective Chief Inspector Jim Dickie, who conducted the manslaughter inquiry, said: "Justice has been done. I am pleased for the victims, especially the Annis family."