The RWC Board will now review venues and put the case for involvement at the Millennium Stadium to the IRB Council.
Lewis said: "We know that England submitted a superb bid and would like to congratulate the Rugby Football Union for all their hard work, but I know South Africa will be disappointed, they are a great rugby nation and I am sure their chance will come again soon.
"Here in Wales we know a lot of hard work lies ahead, we've jumped the first hurdle, now we are all determined to ensure that everyone in world rugby fully understands the importance of the role the Millennium Stadium can play in the success of the 2015 competition.
"The Millennium Stadium is one of the finest rugby venues in the world, thousands of rugby fans based in England are only a short commute from our city centre location and we have the infrastructure, the facilities, reputation and rugby-dedicated population to make a major contribution to the RWC2015 spectacle.
"The reasons for holding matches at the Millennium Stadium are compelling and we remain confident the RFU plan will progress in full.
"We have one of the best rugby stadiums in the world here in Cardiff, the retractable roof ensures games are played in near perfect conditions in front of a capacity of 74,500 fans and its city centre location in Cardiff means it is easily accessible from across Wales and southern Britain."