Eleven babies and one mother died as a result of maternity failings at Furness General Hospital between 2004 and 2013.
A subsequent inquiry report identified 20 failings linked to the deaths.
Health Secretary Jeremy Hunt told the House of Commons that when things go wrong in the future "they will no longer be swept under the carpet".
The inquiry into the Morecambe Bay NHS Foundation Trust - led by Dr Bill Kirkup - found the maternity unit at Furness General had been "dysfunctional" with "substandard care" provided by staff "deficient in skills and knowledge".
It also found working relationships between doctors and midwives were extremely poor, with midwives referring to themselves as "the musketeers" as they pursued normal childbirth "at any cost".
Accepting the findings of Dr Kirkup's report, Mr Hunt said the Nursing and Midwifery Council (NMC) would no longer be responsible for the statutory supervision of midwives in the UK.
He said a decision had been made to move to a model of professional supervision similar to that of other health professionals.
He also promised a new independent NHS patient safety investigation service would be set up by April 2016.
Mr Hunt said a national review of maternity services would continue to look at how safe care could be delivered in geographically isolated areas.
Welcoming Mr Hunt's comments, a spokesman for the NMC said: "As seen through the tragic events at Morecambe Bay, the current set up is open to conflicts of interest, which in not in the best interests of public protection."
Changes to the way midwives are supervised have been announced by the government in response to an inquiry into baby and mother deaths in Cumbria.