The Cyber Schools Programme aims to train 5,700 pupils aged between 14 to 18 over the next five years.
The teenagers will spend up to four hours a week on the cyber curriculum, which will include classroom and online teaching, mixing real-world challenges with hands-on work experience.
The curriculum will be available from September. The Department for Culture, Media and Sport is providing £20m for the extracurricular lessons. DCMS is seeking providers to deliver the programme, with bids closing next month.
Last week MPs warned that a skills shortage was undermining confidence in the UK's cyber defences. Criminal hacking now ranks as one of the top four threats to national security.
In 2015, the Government Communications Headquarters (GCHQ) dealt with 200 national security incidents a month - double the number it was handling in the previous year.
Last year, the Government pledged £1.9bn to a National Cyber Security Centre to counter the rise in cyber crime.
Digital and Culture Minister Matt Hancock said: "This forward-thinking programme will see thousands of the best and brightest young minds given the opportunity to learn cutting-edge cyber security skills alongside their secondary school studies.
"We are determined to prepare Britain for the challenges it faces now and in the future and these extracurricular clubs will help identify and inspire future talent."