A birth unit staffed by midwives opened at the Halifax Road hospital last week as part of a reorganisation of NHS services.
Women expected to have low-risk births which do not require a consultant present are looked after at the unit.
More complex births now happen at a centralised consultant-led maternity unit at Pinderfields Hospital in Wakefield.
Joseph Lloyd was the first baby born at the Dewsbury at 2.59am last Tuesday.
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Mum Amy said: “I delivered in the birthing pool which made the final phase more comfortable for me.
“The care of the midwives was fantastic and they remembered me from my first pregnancy with George.
“I had no worries coming here and it was all very good.”
Caitlin Wilson, consultant midwife at the hospital, said: “I am very happy to welcome Joseph as the first baby to be born at the Bronte Birth Centre.
“I have been leading on the project and it gives me great pleasure to learn of baby Joseph”
The new maternity units at Dewsbury and Pinderfields hospitals opened as part of a restructure at Mid Yorkshire Hospitals Trust.
Emergency surgery has also been centralised at Pinderfields Hospital, which will also become the NHS trust’s main A&E department.
Dewsbury will have an urgent care centre treating minor ailments after next April.