Young people aged between 17 and 21 will get the discounts if they take part in Pass Plus, six extra one-hour training sessions after they have passed their tests. The sessions, at least five of which must be taught on the road, cover driving in and out of town, in all weathers, at night, on dual carriageways and motorways.
At the end of the mini-course, instructors send a completed training record to a new Driving Standards Agency, which issues a certificate of completion to the pupil.
Insurance companies taking part in the Pass Plus scheme will then accept the certificate in exchange for the discount they are offering.
The incentives can be fixed-sum discounts, accelerated no-claims bonuses or reductions on the loadings levied on parents' policies.
The scheme, launched by the Government last week, follows concern over driving standards among young people. Newly qualified drivers can be up to two seconds slower than experienced drivers in recognising danger. One in five will have an accident in their first year.
Tom Moss, controller of Royal Insurance's private motor section, said: "Road accidents are the single biggest cause of death for young people in the UK, so we fully support the scheme. A Pass Plus driver should be better able to handle certain situations and anyone who can show this commitment should be rewarded with lower premiums."
Royal Insurance is offering an immediate one year's no-claims bonus, worth 30 per cent, to Pass Plus certificate holders.
Norwich Union will apply a flat £90 reduction on the cost of comprehensive insurance and £30 for third-party cover.
Premium Search, a 24-hour direct insurance broking service, will give a discount of up to 30 per cent to Pass Plus drivers, depending on the insurer.
For example, a 19-year-old man would normally pay £548 for third-party cover on an Austin Metro. With Pass Plus, his premium for a year would fall to £383.
But the scheme has been given only a qualified welcome by the British School of Motoring, which argues that it still has a number of shortcomings.
Richard Glover, managing director at the BSM, said: "We all know what can happen when new drivers show off to their friends, drive too fast or don't leave enough space to stop or avoid other vehicles and pedestrians.
"However, we feel that Pass Plus scheme may be too much of an extension of the driving test, too prescriptive in its approach, and fails to address fully the real cause of accidents."
Mr Glover said the scheme should focus more on the main causes of accidents among young drivers, namely driver behaviour and risk-perception.