The deceased have been identified as Ritesh Mittal alias Shalu (32) and Amit alias Panda (26).
Jail officials suspect that the two died after consuming some drugs smuggled into the prison. Both the men were lodged in ward number two at jail number 8-9 of the prison complex.
Ritesh was undergoing life imprisonment in a murder case and had spent 11 years in jail while Amit was convicted in an attempt to murder case.
"Authorities called in jail doctors who tried to revive them but realising that they need institutional care and they were sent to DDU hospital where they died at around 9:30 AM," said Tihar DIG and spokesperson Mukesh Prasad.
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After the incident, the head warder responsible for safety of jail ward in which the two convicts were found dead has been placed under suspension and a magisterial probe was ordered.
Jain said growing incidents of violence inside the prison premises indicated serious problems and these should be addressed without any delay.
Jail officials said police were informed about the incident and they have started investigation in the case.
The bodies have been sent for postmortem to ascertain the exact cause of death. A magisterial enquiry will also be initiated in the case, Jain added.
Police will also investigate as to how the drugs were smuggled into the prison complex.
A number of inmates have also lost their lives in the recent past in fights on the jail premises.
A 40-year-old undertrial, Ajay, was stabbed to death on Monday afternoon allegedly by three other inmates over personal enmity.