Context: We describe the new SEPIA (Swedish-ESO PI Instrument for APEX) receiver, which was designed and built by the Group for Advanced Receiver Development (GARD), at Onsala Space Observatory (OSO) in collaboration with ESO. It was installed and commissioned at the APEX telescope during 2015 with an ALMA Band 5 receiver channel and updated with a new frequency channel (ALMA Band 9) in February 2016. Aims: This manuscript aims to provide, for observers who use the SEPIA receiver, a reference in terms of the hardware description, optics and performance as well as the commissioning results. Methods: Out of three available receiver cartridge positions in SEPIA, the two current frequency channels, corresponding to ALMA Band 5, the RF band 158--211 GHz, and Band 9, the RF band 600--722 GHz, provide state-of-the-art dual polarization receivers. The Band 5 frequency channel uses 2SB SIS mixers with an average SSB noise temperature around 45K with IF (intermediate frequency) band 4--8 GHz for each sideband providing total 4x4 GHz IF band. The Band 9 frequency channel uses DSB SIS mixers with a noise temperature of 75--125K with IF band 4--12 GHz for each polarization. Results: Both current SEPIA receiver channels are available to all APEX observers.