The forthcoming Education Bill, expected to become law early next year, will say that governing bodies can only appoint heads who hold the National Professional Qualification for Headship.
But Mrs Morris said putting the regulation into effect will be delayed until there are enough heads with the qualification to give governors a choice.
About 4,000 candidates are expected on the NPQH course in its first year, including some who have been in the pilot scheme. They will take up to three years to complete the course depending on how much training they need.
Every year about 2,500 heads are appointed so the aim is to have at least 5,000 NPQH-qualified heads before enforcing the regulation.
This is unlikely to happen before 2000, although it should beat the 2002 deadline for a professional qualification set by the White Paper Excellence In Schools.
Take-up so far does not reflect the gender balance of deputy heads, the qualification's target audience. Women candidates from secondary schools are over-represented, while their primary school colleagues are under-represente d. Just over half the overall candidates - 55 per cent - are female.
There are about five times as many primary schools as secondaries, though this is not reflected in the numbers signing up to the NPQH. Of those starting the course now, there are 1,694 primary teachers and 1,218 from secondaries.
Mrs Morris told 200 NPQH students, heads and trainers that the qualification was at the heart of the Government's schools strategy. "We believe the Government's targets and the agenda for raising standards can be achieved only if there is a substantial programme of reskilling and updating the knowledge of serving teachers and headteachers," she said.
Training should be combined with studying management in industry to produce a qualification built on on best practice, she said.
She welcomed the TTA's decision to hold an annual event to recognise the work of the best teachers and heads. The TTA is commissioning independent advisers to review the NPQH to make sure it is working effectively. An interim report is expected early next year.
The TTA is trying to ensure standards of training and assessment operated by regional centres are consistent, and that the qualification recognises candidates' existing skills. It is considering a fast-track course for those showing early signs of leadership qualities
The agency also wants to boost the number of primary teachers applying to take the NPQH.