The new 75,000-capacity covered venue would cost pounds 104m overall and play host to the Rugby Union World Cup finals, which will be held in 1999.
National Lottery money would be channelled through the Millennium Commission as part of celebrations to mark 2000. The rest would be raised privately.
According to a survey commissioned by the bid's organisers, the Welsh Rugby Union, seven out of 10 Welsh people support the scheme in preference to a rival bid to develop the Cardiff Bay Opera House.
The new hi-tech arena, built on the site of Cardiff Arms Park, would be a so-called "third generation" stadium which could also host other entertainments. Bid organisers who commissioned the MORI poll unveiled their revised plan yesterday. A previous bid had failed to incorporate enough of the existing structure and plans to develop the nearby Cardiff Athletic venue had been shelved, the project's designer said.
Russell Goodway, leader of South Glamorgan and Cardiff County Council , which backed the bid, hailed the project as the people's choice which had now met the requirements of the commission.
He said: "Our next step is to take the people's choice back to the commission next week with the revised bid highlighting its huge economic, cultural and social regeneration opportunities for Cardiff and Wales."
While the Department of National Heritage has not ruled out accepting both schemes under the Millennium scheme, it is thought highly unlikely that both will be successful.
The stadium bid is due to be presented to the commission on 15 November.