It would create 21 new unitary councils to replace the current eight counties and 45 districts.
Welsh Secretary John Redwood said he expected the Bill to be on the statute book before the summer recess.
The Bill is based on the proposals set out in the reorganisation white paper, with a few name and boundary changes which the Welsh Office says show Mr Redwood has listened carefully and sympathetically to many representations.
Names - the Glamorgan Valleys authority will be called Rhondda, Cynon and Taff ; Powys is to be known as Mid Wales; and West Glamorgan is to be known as Neath and Port Talbot.
Boundaries - Flintshire is expanded to include all of Delyn; Cynwyd and Llandrillo will be incorporated in Denbighshire; Ystradgynlais and Tawe Uchaf will not be split off from Mid Wales; Coychurch Lower will remain in Bridgend; and Llanelly (Gwent) moves from the Heads of the Valleys to Mid Wales.
Mr Redwood's proposal that unitary councils could seek to delegate the management of local services to smaller areas within the authority has also been included in the Bill.
Another change announced last week is an increase in the number of council members from 1,100 to about 1,250.
Mr Redwood said: 'I was persuaded by the arguments of the district councils that 1,100 councillors would not enable proper representation in every area. In deciding on a figure of about 1,250 I have taken account of the importance of councillors' constituency role and that the number of authorities is being more than halved'.