He is specifically targeting non-profit community based organisations "responsive to the needs of the community".
The winning organisation will be given a grant worth up to £500,000 and will be expected to seek further financial backing to build and sustain the event for the future.
Waiving the fee to use Trafalgar Square and assistance from a GLA events officer would bring total support to around £650,000.
The Mayor's Office is already the main sponsor of the event, which takes place each year in early July and attracts hundreds of thousands of people from across the UK and around the world.
"London's Pride celebrations are a key event in our city's cultural calendar. They attract not just Londoners, but people from across the UK and around the world, contributing to a tourism sector that generates billions for our economy and creates thousands of jobs," said Johnson.
"I am proud of London's reputation as a dynamic world city in which LGBT people can be who they are and it is only right that we should host a high profile celebration to rival other major Pride celebrations around the world."
Organisations should email their initial interest to . The winning bid is expected to be announced in early 2013.
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