The Batley and Spen MP, who died after an attack in June, cut the turf at a ceremony to mark the start of construction on the £1.38m facility last December.
Yesterday her parents Jean and Gordon Leadbeater and her sister Kim officially opened the new midwife-led Bronte Birth Centre at Dewsbury Hospital.
Her mother said they were very pleased and proud to represent her.
“We know it was very dear to Jo’s heart and she would have been very proud to have been here,” Mrs Leadbeater added.
“Jo was an MP, a humanitarian, a wife, a sister, a daughter, but most of all she was a mum, and she would have just been amazed at the birth unit and she knew how important it was to have units like this in our local community.”
The MP was herself born at the Dewsbury Hospital site in 1974, in what was then Staincliffe Hospital, and the mother-of-two was a strong supporter of empowering women and providing services locally.
Her family chose a quote featuring on artwork in the new centre, which houses six birthing suites and aims to offer mothers who are unlikely to require medical intervention personal, one-to-one care in a homely environment.
Jules Preston, chairman of The Mid Yorkshire Hospitals NHS Trust, said: “It was a great privilege to host the family of Jo Cox MP and the dedication plaque provides a permanent legacy of her valuable work with the trust representing the interests of local people.”
So far, 20 babies have been delivered at the unit, which is one of two new midwife-led units created as part of a reorganisation of hospital services in Dewsbury, Wakefield and Pontefract.