The death of Dominic Comfort followed two others during November, including the murder of convicted killer Liam Deane.
Independent investigations are being carried out into each of the deaths, while police are conducting a criminal investigation into allegations of sexual assault by a prisoner.
News of the earlier deaths had prompted concerns about overcrowding from the Howard League for Penal Reform and East Leeds MP Richard Burgon, who is also Shadow Justice Secretary.
Mr Comfort had been on remand when he was found in his cell after an apparent attempt to take his own life on November 13.
The 33-year-old, of Woodview Street, Beeston, eventually passed away on November 22.
A Prison Service spokesman said: “HMP Leeds prisoner Dominic Comfort died in custody on November 22.
“As with all deaths in custody there will be an independent investigation by the Prisons and Probation Ombudsman.”