The new contracts, worth a combined total of £12m a year, will see education provision extended from 15 hours to around 30 hours each week.
The Manchester College has been contracted to provide education at Cookham Wood YOI in Kent, Werrington YOI in Stoke, and Wetherby YOI in West Yorkshire, while Prospects has been contracted to deliver education at Feltham YOI in West London.
Of the other two YOIs that currently hold under-18s, Hindley near Wigan is due to stop taking juveniles from March 2015, and Parc in South Wales is privately run by G4S and has its own education arrangements.
The government has said the contracts will result in young people in custody receiving the same quality of education as in mainstream school and college.
Maths, English and computing will be taught in classrooms, while vocational education will also be available, alongside physical education and work experience opportunities.
Youth justice Minister Andrew Selous said the time young offenders spend in custody can be one of the only opportunities to “turn their lives around and prevent them reoffending”.
“High-quality education and training in the youth estate is absolutely vital, which is why we are reforming the culture of YOIs to put learning at the centre and doubling the amount of time young offenders spend in the classroom," he added.
“These new contracts will help drive up standards across the youth estate and give young people the right skills and training to lead productive lives, free from crime.”
The new contracts form part of government efforts to drive down reoffending rates by “placing education at the heart of youth custody”.
The government is planning to open a 320-bed secure college, described as a "fortified school" and run by a head teacher alongside a leadership team made up of educational professionals and offender managers, in Leicestershire in 2017.
It hopes that secure colleges will eventually replace current provision in YOIs and secure training centres.