Osborne will say that the old system of governing from London "is broken" and has led to imbalances in economy.
The outlined proposals are also expected to be included in the Queen's speech before the parliament at the end of May.
Greater Manchester will elect a mayor directly for the first time in 2017. The direct vote was agreed on in 2014, following consultations between George Osborne and leaders of 10 local councils.
Up to now, most mayors in Britain have been elected by town or city councils and had only restricted powers.
In 2000, the Local Government Act introduced direct elections to the mayor office in a small number of areas. London has been the most prominent example of directly elected mayors, holding direct elections to the post since 2000.