The competition will see the capital's 32 boroughs bid for more than
£1m of funding to stage a programme of cultural events and initiatives.
It will be supported by a grant of £300,000 from City Bridge Trust, part of the City of London Corporation.
The London Borough of Culture award is part of the mayor's plans to support the arts in London.
Two boroughs will be crowned winners in February, taking the title of London Borough of Culture for 2019 and 2020 respectively.
Hall said the winning boroughs would be "chosen based on their artistic
vision and ambition to deliver outstanding cultural initiatives in
their local area, putting communities at the centre of the programme's
design and delivery".
Several cultural institutions will provide
help to the boroughs, including the Barbican, the Museum of London, the
Roundhouse, Film London and the National Trust.