Mr Browne said at an event at the Royal School Armagh: 'The Irish Rugby Football Union believes that Ireland, and its people, will make the perfect hosts for the 2023 Rugby World Cup.
'We believe it is opportune for us now to put forward Ireland's undoubted credentials to host world rugby's showpiece.'
The political administrations north and south have been engaged in a preliminary assessment exercise over the last 10 months to weigh up the feasibility of submitting an official bid.
In February, former Irish international star Hugo MacNeill was asked to chair the cross-border working group examining the issue.
As well as the traditional rugby stadiums such as the Aviva in Dublin, the Kingspan at Ravenhill in Belfast and Thomond Park in Limerick, a 2023 World Cup in Ireland would hope to utilise a number of impressive Gaelic football venues, including the 82,300-capacity Croke Park in Dublin.
Mr Kenny said the Irish Government was fully behind the bid.
'I am delighted to formally announce the Government's support, in conjunction with the Northern Ireland Executive, to formally back the IRFU's bid to host the 2023 Rugby World Cup,' he said.
'Ireland will put together a winning bid that will be impossible to resist. We have the fans, the stadiums, and the accessibility to make it a World Cup to remember.'