The new Local Government Bill being detailed on Friday will also repeal Section 28, the law that prevents local authorities describing homosexuality as a normal way of life.
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Other options included in the bill are an indirectly-elected leader, picked by the council, who would head a cabinet.
Boosting turnout
Local Government Minister Hilary Armstrong said directly-elected mayors would have the benefit of increasing turnout in local elections which is extremely poor in England and Wales when compared with the rest of the European Union.
She told the BBC that mayors would also enable electors to know who to hold accountable for the state of local services.
Ms Armstrong said: "No-one can be complacent about the low level of interest in local democracy."
The minister also acknowledged that local councillors had "anxieties" about the proposals, which some fear will undermine their power.
European norm
But she added: "If you go to other European countries, indeed the rest of the world, where these models are much more the norm, local councillors do not feel they are undermined and have nothing to do.
"Under our proposals, the role of councillors ... is going to be much enhanced."
The bill will also introduce a new ethical framework for local government.
New codes of conduct will be put in place and they will be overseen by local standards committees directed by a new independent agency - the Standards Body.
The Standards Body will investigate complaints of misconduct.
Where allegations are upheld sanctions include disqualification from office.