METIS is the Mid-infrared Extremely large Telescope Imager and Spectrograph, one of the first generation instruments of ESO's 39m ELT. All scientific observing modes of METIS require adaptive optics (AO) correction close to the diffraction limit. Demanding constraints are introduced by the foreseen coronagraphy modes, which require highest angular resolution and PSF stability. Further design drivers for METIS and its AO system are imposed by the wavelength regime: observations in the thermal infrared require an elaborate thermal, baffling and masking concept. METIS will be equipped with a Single-Conjugate Adaptive Optics (SCAO) system. An integral part of the instrument is the SCAO module. It will host a pyramid type wavefront sensor, operating in the near-IR and located inside the cryogenic environment of the METIS instrument. The wavefront control loop as well as secondary control tasks will be realized within the AO Control System, as part of the instrument. Its main actuators will be the adaptive quaternary mirror and the field stabilization mirror of the ELT. In this paper we report on the phase B design work for the METIS SCAO system; the opto-mechanical design of the SCAO module as well as the control loop concepts and analyses. Simulations were carried out to address a number of important aspects, such as the impact of the fragmented pupil of the ELT on wavefront reconstruction. The trade-off that led to the decision for a pyramid wavefront sensor will be explained, as well as the additional control tasks such as pupil stabilization and compensation of non-common path aberrations.