Even when universities formally require staff on probation to gain a qualification, the rule is not always enforced because research can take priority, Craig Mahoney will tell a conference in London this week.
Professor Mahoney will also set out plans for all universities to review their policies on promotions to ensure that they recognise staff efforts in teaching.
A recent study - described as "shocking" by David Willetts, the universities and science minister - found that pedagogy came a poor second in UK university promotions, with teaching criteria often entirely absent from institutional policies.
Professor Mahoney will tell the Enhancing the Student Experience conference on 11 November that while he does not agree with all of the Browne Review's recommendations, he "wholeheartedly" supports the proposal that all new academics who teach should undertake a teaching qualification.
He believes that as well as providing a benchmark for individuals, a qualification would give the general public and students confidence that they are being supported by "competent professionals".
"At present, there is some inconsistency. Not all institutions require probationary academic staff to undertake a postgraduate certificate in higher education or the equivalent," he will say.
"Even where there is a formal requirement, this may not always be enforced - where, for example, as part of probationary procedures, research activity and outputs become prioritised above completion of a teaching-related qualification."
He will add that there may also be "significant variation" in the length and content of training courses.
But Professor Mahoney will warn that the qualification must not simply become "a box-ticking exercise".
A consultation document on the UK Professional Standards Framework, to be launched in a few weeks' time, will propose that all higher education institutions review their practice to ensure that their promotional criteria and procedures "take full and clear account" of high-quality teaching.
Universities should also adopt teaching-related criteria in their promotional processes "where appropriate", and be expected to use the revised framework to ensure that teaching is given "parity of esteem" with other academic responsibilities.
Professor Mahoney will also raise doubts about the value of information on course contact hours - information the government will soon require universities to publish.
"Whatever we might think about this type of intervention - and the link between contact hours and quality is highly dubious - the message is clear: the quality of teaching and learning for all students is top of the agenda," he will tell delegates.
The event was co-organised by the 1994 Group of small research-intensive universities.