New father Jamal Mahmoud died after he was stabbed at the north London jail during an attack that also injured two others on Tuesday.
Basana Kimbembi, 34, will appear at court at a later date to answer the murder charge, police said.
A second man, 26, has been released from custody over the incident and returned to prison.
The two injured men - aged 21 and 30 - were taken to an east London hospital for treatment for non-life threatening injuries, police said, and they remain there.
A man has been charged with murder following the death of a 21-year-old man at Pentonville Prison.