The announcement comes four months after the trust was fined £1.6m for "avoidable failings" connected to the deaths of three babies in 2021.
Campaigners Dr Jack and Sarah Hawkins, parents of Harriet who was stillborn in 2016, said the development was "one piece of the jigsaw towards accountability".
They added: "Harriet should be nine years old. Our lives were completely destroyed by the unimaginable and repeated trauma at the hands of NUH.
"A prosecution for corporate manslaughter will only penalise the trust, not the individuals responsible, many of whom are still working today.
"We must never lose sight of individual accountability for those who so cruelly stole not just our daughter's life and voice, but many others."
A joint statement from the hospital trust's chair Nick Carver and its chief executive Anthony May said: "Since joining the board, we have emphasised the importance of openness, transparency and accountability in our leadership and decision-making. We recognise that there is more to do.
"We are fully committed to the ongoing police investigation and the Independent Review of Maternity Services, led by Donna Ockenden.
"We would like to reassure the public that we are determined to improve our maternity services.
"We know how important the police investigation and independent review are for the affected families, the trust and our local communities. We hope that affected families receive the answers that they deserve."