For the construction of high-precision optical assemblies, direction and position measurement and control of the involved laser beams are essential. While optical components such as beamsplitters and mirrors can be positioned and oriented accurately using coordinate measuring machines (CMMs), the position and direction control of laser beams is a much more intriguing task since the beams cannot be physically contacted. We present an easy-to-implement method to both align and measure the direction and position of a laser beam using a CMM in conjunction with a position-sensitive quadrant photodiode. By comparing our results to calibrated angular and positional measurements we can conclude that with the proposed method, a laser beam can be both measured and aligned to the desired direction and position with 10 μrad angular and 3 μm positional accuracy.