The Integration and Verification Testing of the Large Synoptic Survey Telescope (LSST) Camera is described. The LSST Camera will be the largest astronomical camera ever constructed, featuring a 3.2 giga-pixel focal plane mosaic of 189 CCDs with in-vacuum controllers and readout, dedicated guider and wavefront CCDs, a three element corrector with a 1.6-meter diameter initial optic, six optical filters covering wavelengths from 320 to 1000 nm with a novel filter exchange mechanism, and camera-control and data acquisition capable of digitizing each image in two seconds. In this paper, we describe the integration processes under way to assemble the Camera and the associated verification testing program. The Camera assembly proceeds along two parallel paths: one for the focal plane and cryostat and the other for the Camera structure itself. A range of verification tests will be performed interspersed with assembly to verify design requirements with a test-as-you-build methodology. Ultimately, the cryostat will be installed into the Camera structure as the two assembly paths merge, and a suite of final Camera system tests performed. The LSST Camera is scheduled for completion and delivery to the LSST observatory in 2020.