Britain is the first member of the G7 to apply to join the AIIB, which will be formally established by the end of 2015.
"Joining the AIIB at the founding stage will create an unrivaled opportunity for the UK and Asia to invest and grow together," said UK Chancellor of the Exchequer George Osborne.
However, officials from the US signaled their unhappiness about the UK's decision to pursue greater economic engagement with China through the organization, and repeated criticism US State Department spokesperson Jen Psaki voiced last year that the project did not "meet international standards of governance and transparency.