Writing in the Mail on Sunday, Johnson said the measure would also let him to deliver on his campaign pledge to enact tougher sentencing laws for serious sexual and violent offenders, and for those who carry knives, Bloomberg reported.
The prime minister will host a discussion in Downing Street on Monday to discuss improving the criminal justice system, with police chiefs, judges and prison bosses.
According to government data, 62% of prisons in England and Wales are overcrowded.
“The prime minister is putting prisons at the heart of our bold plan to create a justice system which cuts crime and protects law-abiding people.
More and better prison places means less re-offending and a lower burden on the taxpayer in the future,” said justice secretary Robert Buckland.