Installation will begin in spring 2020, with all scanners expected to be in place by the summer.
Images produced by the scanner provide a level of detail inside the body that has not been seen before in the Prison Service.
In tests at HMP Leeds the scanner found over 300 smuggled items and, in its first year, has slashed the number of drugs getting into the prison.
The use of X-ray body scanners at 10 other challenging prisons was successful in detecting contraband and contributed to a significant reduction in violence and drug use.
“This is fantastic news,” said Ms Hernandez. “I wrote to the previous Minister to prioritise HMP Exeter due to the levels of violence and drug-taking.
“Drugs are rife in British prisons, criminality is allowed to flourish, and gangs exploit fundamental weaknesses in security to carry out their illegal activity.
“Ex-offenders will stand a much better chance of leading fulfilling and productive lives if they have experienced rehabilitation and support while in the care of the Prison Service.”