Voters in John Alexander's seat of Bennelong will head back to the polls for a by-election on December 16, after the Liberal MP resigned over concerns he may be a British citizen.

A second House of Representatives by-election would further threaten the Coalition's stability, after it lost its majority when former deputy prime minister Barnaby Joyce was disqualified from Parliament.

The announcement came as the Government and the Opposition struck a deal on how to try and resolve the ongoing citizenship saga.

Rolls will close Monday November 20 and nominations close Thursday November 23.

The seat of Bennelong has been a crucial one in past elections.

In 2007, then prime-minister John Howard lost to Labor's Maxine McKew, the same year Kevin Rudd became prime minister.

The migrant vote would play a decisive role in determining the outcome of the Bennelong by-election.

Home to people from dozens of countries, the seat in Sydney's north-west is one of the most diverse in the federal parliament.

More than half of Bennelong's population was born overseas and its demographic has changed dramatically in the past decade, which is also due to a boundary change.

The current electorate of Bennelong encompasses the suburbs of Denistone, Denistone East, Epping, East Ryde, Eastwood, Macquarie Park, Marsfield, Meadowbank, Melrose Park, Putney, North Epping, North Ryde, Ryde, West Ryde and parts of Carlingford, Ermington and Gladesville, in the North Western suburbs of Sydney.