The force has also bought a one-year subscription to evidence.com, a cloud-based digital evidence management platform.
Evidence collected from the cameras is stored and managed on the platform rather than on in-house servers.
The 'small but highly visible' AXON cameras were developed by TASER and can be attached to uniforms, sunglasses, collars or headgear.
When recording they capture a wide-angle, colour picture of what an officer is facing, which is then automatically uploaded to evidence.com when placed on a docking station.
A number of forces are already trialling or deploying body-worn video cameras. The Met Police is set to issue 16,000 officers with cameras by spring 2016 after a trial of 500 devices that started last year.
Devon and Cornwall police were the first to try out the new technology in 2006. The cameras are currently being rolled out across a number of forces, including those in Durham, Hampshire, the West Midlands and Greater Manchester.
"The City of London is currently undergoing a transformation in how we use technology to assist us with keeping the City safe," said chief superintendent Dave Lawes.
"We're excited about TASER's end-to-end solution that allows our police force the flexibility to integrate with existing and future technology."
The force is the smallest in England and Wales, policing an area of just 1.12 square miles with 1,310 employees including 750 full-time police officers.