An independent review, published in March, warned teacher training had deteriorated over the previous decade.
On Tuesday, Mr Lewis also announced education degrees would be studied over four years rather than three.
Plaid Cymru said too many universities were offering teacher training courses and this was reducing standards.
"In return for that extra level of effort what we will also be offering - and this is my ambition - we will be offering the best teacher training in the UK without any doubt at all," Mr Lewis told BBC Wales.
He said trainee primary school teachers would specialise in certain subjects.
"For a very long time we've had too few subject specialists in our primary schools - people teaching mathematics that may not be entirely comfortable with mathematics," he said.
"We have to redesign that primary teachers course to ensure every primary teacher has a subject specialism built in."
Plaid Cymru education spokesman Simon Thomas said it was "disappointing" that in a statement to AMs Mr Lewis had been "silent" on whether "the delivery of teaching training needs to be streamlined".
This year, 2,700 teachers are being trained at three centres involving five universities in Wales.
Mr Thomas said: "Can we continue to have so many colleges providing teaching training when some struggle to maintain the highest standards and how can we develop expertise in this field in Wales?"
Liberal Democrat AM Aled Roberts welcomed ministers' "acknowledgement of the report's recommendations", but expressed concerns about how the plans would "work in practice" and questioned whether the resources needed would be provided.
It will become harder to qualify to be a teacher in Wales, but teacher training will be the best in the UK, Education Minister Huw Lewis has said.