The centre is the size of ten football pitches and is situated in Swansea Bay. In all, the site will create as many as 1,200 full-time jobs over five years with another 1,500 seasonal jobs.
Rhodri Morgan, First Minister for Wales, said that the opening of the centre was a major boost for the Welsh economy and represents the single biggest investment in Wales since Devolution in 1999.
Morgan said: "The speed of delivery of this project has been exceptional. It is an absolutely textbook example of how to do regional economic development. Amazon is one of only a handful of truly world brands that have emerged since the internet changed the way we live our lives.
"To have such a big name in e-commerce set up a major European base in Swansea Bay is an outstanding achievement for Wales."
The warehouse in Swansea is the online retailer's fourth in the UK. It already has two in Scotland, Glenrothes in Fife and Gourock in Inverclyde, and one in Milton Keynes, England.
The opening of the centre follows the Office of Fair Trading clearing the proposed acquisition of Amazon's online DVD rental service in the UK by LoveFilm.
The OFT said that while it had competition concerns about the merger, which will control 90% of the online DVD market, it concluded that LoveFilm had no incentive to worsen its customer proposition because of the competition it faced from an array of other providers of video content.'
Simon Pritchard, OFT senior director of mergers, said: "Under the statute, we decide cases based on evidence rather than intuition. While we fully expected LoveFilm to argue that it faces competition from a wide variety of players, our decision was based squarely on what the documents told us."