This paper presents an integrated system for performing precision harvesting missions using a legged harvester. Our harvester performs a challenging task of autonomous navigation and tree grabbing in a confined, GPS denied forest environment. Strategies for mapping, localization, planning, and control are proposed and integrated into a fully autonomous system. The mission starts with a human mapping the area of interest using a custom-made sensor module. Subsequently, a human expert selects the trees for harvesting. The sensor module is then mounted on the machine and used for localization within the given map. A planning algorithm searches for both an approach pose and a path in a single path planning problem. We design a path following controller leveraging the legged harvester's capabilities for negotiating rough terrain. Upon reaching the approach pose, the machine grabs a tree with a general-purpose gripper. This process repeats for all the trees selected by the operator. Our system has been tested on a testing field with tree trunks and in a natural forest. To the best of our knowledge, this is the first time this level of autonomy has been shown on a full-size hydraulic machine operating in a realistic environment.