If the provisional licence is successful, full licences could be thrown away for digital ones.
Mr Shapps said EU rules had stopped the introduction of digital licences and the move is part of "exciting new post-EU freedoms".
He said: "This is a golden chance to shake off the bureaucracy, invest in our future and realise our potential with world-leading transport that benefits all of Britain."
In its plan for 2021-2024, the DVLA said: "We will introduce a digital driving licence for provisional drivers and also start to build a customer account facility.
"This will ultimately give our customers personalised, easy and secure access to a range of services and allow them more choice in how they transact with us.
"Our services will be secure, scalable and resilient and we will continue to explore and expand the use of emerging technologies."
But driving charities and firms warn the new plans could encourage more crimes of fraud.
Steve Gooding, director of motoring research charity the RAC Foundation, said: "These days the one thing drivers are most likely to have with them is their phone, so using it to carry their driver's licence could be quite handy.
"The risk is that the more personal data we store on our phones the more tempting a target they become for thieves and hackers."
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