Ofqual's outgoing chief executive Isabel Nisbet said retaining traditional writing materials would mean GCSEs and A-levels becoming "invalid" for digitally native pupils.
Two major exam boards have given enthusiastic support to her call for reform.
Edexcel managing director Ziggy Liaquat said: "Technology has the potential to transform education by making its delivery more personalised, efficient and effective and more transparent and secure.
"The examination system is yet to fully realise this potential."
And the AQA board said it was "really encouraged" that Ofqual was "taking the issue so seriously".
Millions of exam scripts are already scanned in and marked online every year.
But Ms Nisbet is concerned that increasingly "techno savvy" pupils can take only "bits" of a "very small" number of GCSEs and A-levels on computers by.
She said she fears that if school exams do not go online soon then exam preparation "will become a separate thing to learning" for candidates used to working on computers.
"They use IT as their natural medium for identifying and exploring new issues and deepening their knowledge," she writes in today's TES.
"Yet we are even now accrediting new GCSEs, due to run for several years, which are still taken largely on paper.
"This cannot go on. Our school exams are running the risk of becoming invalid, as their medium of pen and ink increasingly differs from the way in which youngsters learn."
Examination Officers' Association chief executive Andrew Harland said computerisation "would revolutionise the system".
"The technology just speeds the whole process up, reduces human error and could allow instantaneous responses and grades."
But he warned it might not suit pupils with special needs and that while exam boards and Government could benefit from reduced costs, schools would need considerable investment.
OCR chief executive Mark Dawe, said even moving elements of GCSEs and A- levels online would "take some time".
"How do you ensure that there is fairness across every centre in the country?" he said.
"All the networks have got to be robust, every learner has to have access to a computer of the same speed because what if one takes twice as long to recognise typing as another?
"You have got to install security - there are real challenges about general exams being done by IT."
In 2004, Ms Nisbet's predecessor said most exams would be computerised by 2010. But Ms Nisbet said it had been an "aspiration without a plan".
The Department for Education said it did not have a view on the computerisation of exams or want to be drawn into the debate.
`SHADY PRACTICE' - Call to root out grade nudgers
Teachers have a "professional duty" to help expose "shady practice" in schools, the exams regulator said.
Isabel Nisbet said they should help uncover those who "crossed the line" of what was acceptable in trying to increase grades.
"Join with us in shaming out of the system shady practice involving the wrong kind of help to nudge students' grades upwards," she writes in today's TES.
"I am fully aware of the tensions and temptations from high-stakes accountability systems. But professionalism means assessing validly and fairly."
Ms Nisbet gave one example of a school that had helped on English coursework to a point where it "really was telling (pupils) what to put".