We present a fully-integrated sensing and control system which enables mobile manipulator robots to execute building tasks with millimeter-scale accuracy on building construction sites. The approach leverages multi-modal sensing capabilities for state estimation, tight integration with digital building models, and integrated trajectory planning and whole-body motion control. A novel method for high-accuracy localization updates relative to the known building structure is proposed. The approach is implemented on a real platform and tested under realistic construction conditions. We show that the system can achieve sub-cm end-effector positioning accuracy during fully autonomous operation using solely onboard sensing. contributed to the state estimation and high accuracy localization {blumh, gawela, rsiegwart}@ethz.ch. Timothy Sandy contributed to the state estimator, and motion control tsandy@ethz.ch. Koen Krämer, Johannes Pankert, Farbod Farshidian, Marco Hutter contributed to the Motion planning and control {kokraeme, pankertj, farshidian, mahutter}@ethz.ch. Selen Ercan, Fabio Gramazio contributed to the building task interface {ercan, gramazio}@arch.ethz.ch.