Bill Rammell, a former higher education minister, says it would be fairer and more efficient than predicting grades.
He says there is already a growing trend for students to apply for the first time during clearing.
But Universities UK has rejected suggestions there will be any "chaotic scramble" for places this year.
A-level results in England, Wales and Northern Ireland are to be published on Thursday, with a record 655,000 applicants waiting to find out about university places.
Mr Rammell, vice-chancellor of the University of Bedfordshire, says there should be a longer-term aim to move to a system of applying after students know their results - so-called "post-qualification application" - rather than the current system of relying on predicted grades to receive conditional offers.
"If you started afresh you wouldn't have this elaborate system of predicted grades," he said.
But in the shorter term Mr Rammell says there are growing pressures from students which are already pushing the system towards post-qualifications applications.
He says that at his university he has already seen a growing number of students applying for the first time during clearing once they know their A-level results, rather than by the initial mid-January deadline.
Students are able to begin applications during clearing, which also provides a back-up system for those who missed out on their required grades.
Research from the admissions service, Ucas, has shown that about half of A-level grades predicted by teachers are incorrect.
Although a formal switch to a post-results system might not be imminent, he says the pressure of students who are applying late will "effectively push it in that direction".
As a higher-education minister under the Labour administration, Mr Rammell said he had been a "strong advocate" of the admissions system being moved.
If students knew their grades when applying it would be simpler, he says, and he believes the current system based on predictions is more likely to work against poorer students.
Mr Rammell says there had been "conservative forces" opposed to such a change, which could mean alterations to the timing of the exam system or the start of the autumn university term.
He says the major change in admissions in recent years has been that students, with their tuition fee, have a much stronger position in looking for places.
In the past, he says universities were choosing students, now it was much more a case of students choosing where they would like to study.
But he warns against the use of "retail gimmicks" to attract students and argues that recruitment should be based on offering a better student experience.
Nicola Dandridge, chief executive of Universities UK, says universities are ready to handle record numbers of applications this week, with the limit on places removed this year.
"Despite the annual predictions that there will be a chaotic scramble for places, universities are, as always, prepared for the busy undergraduate admissions period," said Ms Dandridge.
And she said it was important that the clearing process, used by 61,000 students last year, should not be seen as a "second-best option".
Ucas says that clearing provides a route for those who want to apply after they get exam results.
And the admissions service suggests consultation on this had found "significant practical challenges" in implementing an admissions process after A-level results.
The university admissions system should be switched so applications are made after students know their exam results, says a university vice-chancellor.