The new system will also allow motorists to spread the charge in monthly instalments instead of paying in a lump sum once a year or every six months. However, paying in monthly instalments will cost 5% more overall than paying the duty annually.
The Chancellor said it signalled a move "into the modern age" and the move was welcomed by the AA, which said it would "save money that can be better spent on improving other DVLA services".
The organisation added: "The AA will examine the proposals and ensure drivers still have some form of receipt other than a tax disc. We also warmly welcome the idea of allowing monthly payments for car tax - this will help ease the burden of annual fixed motoring costs, which, for some, often come all at once."
Jonathan Evans, a tax expert for professional services firm PwC, added: "This will make things easier administratively, although it is not a big change. Many people already renew their tax discs online so this is a logical step.
"However, there will be people who do not have access to electronic payment systems or computers so provision will be needed for these people to tax their vehicles. With modern copying equipment it must be simple to produce fake tax discs, so it seems a sensible anti-fraud measure."
The paper disc, along with vehicle excise duty, was introduced in 1921. Its original role was to pay for the building and upkeep of roads, but since 1937 the proceeds have been pooled in a single Treasury pot.
The DVLA said the body got about 160,000 reports from people of potentially untaxed vehicles last year, and put the rate of fraud at about 0.6% - equivalent to about 16,000 motorists in Scotland.