The merger of the two bodies is part of the Government's programme for the rationalisation of State agencies.
The Sport Ireland Bill is available to view on the Department of Transport, Tourism and Sport website here.
Minister Michael Ring TD said: "This Bill brings responsibility for the implementation of Irish sports policy under a single agency, Sport Ireland. The new agency will take over responsibility for the relevant functions currently performed by the Council and the Authority.
"Sport Ireland will continue the work currently being done by the Council in promoting, developing and co-ordinating sport in Ireland and also the work of the Authority in developing the National Sports Campus at Blanchardstown. I hope to have the Bill enacted during the next Dáil term and to establish Sport Ireland as early as possible."
The Sport Ireland Bill combines the main provisions of the Irish Sports Council Act, 1999 and the National Sports Campus Development Authority Act 2006.
It also includes new provisions relating to doping in sport, which ensure the statutory underpinning of the national Anti-Doping Programme and the Irish Anti-Doping Rules.
Minister Ring added: "Anti-doping is a key area of work in sport aimed at ensuring that all athletes are competing on an equal footing. The Bill includes new provisions which will help Sport Ireland in its work in combating doping in sport, and in continuing the work done by the Irish Sports Council in this area.
"The Bill provides a statutory basis for Ireland's Anti-Doping Programme and the Irish Anti-Doping Rules. It also provides for sharing of information between Sport Ireland and relevant organisations, including the Irish Medicines Board, the Gardaí and Customs, which is an essential element in the fight against doping in sport."