The £18.5m building has taken 18 months to complete and includes exhibition spaces, a cafe and shops.
Walks and trails around the site have also been upgraded, with the addition of a new accessible cliff-top walk for families and people with disabilities.
The decision to rebuild the centre follows years of controversy after the original centre burned down in 2000.
The new centre will have longer opening hours over the summer and will be serviced by a park-and-ride facility from Bushmills.
The state-of-the-art complex is hidden from the coastal landscape by a grass roof.
Among the dignitaries attending the opening on Tuesday were the first and deputy first ministers, Peter Robinson and Martin McGuinness.
Max Bryant of the National Trust said the centre was "a whole new experience for visitors".
"They can go through and enjoy the active interpretation area, before picking up the free audio guide, voiced by local actor Conleth Hill, and take that to the stones," he said.
Standard admission to the centre costs £8.50 for adults and £4.25 for children. A family ticket for two adults and up to three children costs £21.
The design for the centre has been inspired by the Causeway's 40,000 hexagonal basalt stones and the stories of the legendary giants, Finn McCool and Benandonner.
In 1986, Unesco declared the Giant's Causeway to be a World Heritage Site.
In 2007, Northern Ireland's then Environment Minister, Arlene Foster of the DUP, announced she was minded to let property developer Seymour Sweeney's company Seaport Investments Ltd build the centre.
However, that decision was reversed months later.
In January 2009, Mrs Foster's ministerial successor, Sammy Wilson, gave approval to the National Trust's plan for new facilities.
In May 2009, Mr Sweeney dropped a legal challenge to the government's handling of rival bids to build the centre, which cleared the way for work to begin on the National Trust's plans.
The National Trust's Giant's Causeway visitors centre on the north Antrim coast has opened to the public.