The KATRIN experiment aims for the determination of the effective electron antineutrino mass from the tritium beta-decay with an unprecedented sub-eV sensitivity. The strong magnetic fields, designed for up to 6 T, adiabatically guide, beta-electrons from the source to the detector within a magnetic flux of 191 Tcm(2). A chain of ten single solenoid magnets and two larger superconducting magnet systems have been designed, constructed, and installed in the 70m-long KATRIN beam line. The beam diameter for the magnetic flux varies from 0.064 m to 9 m, depending on the magnetic flux density along the beam line. Two transport and tritium pumping sections are assembled with chicane beam tubes to avoid direct "line-of-sight" molecular beaming effect of gaseous tritium molecules into the next beam sections. The sophisticated beam alignment has been successfully cross-checked by electron sources. In addition, magnet safety systems were developed to protect the complex magnet systems against coil quenches or other system failures. The main functionality of the magnet safety systems has been successfully tested with the two large magnet systems. The complete chain of the magnets was operated for several weeks at 70% of the design fields for the first test measurements with radioactive krypton gas. The stability of the magnetic fields of the source magnets has been shown to be better than 0.01% per month at 70% of the design fields. This paper gives an overview of the KATRIN superconducting magnets and reports on the first performance results of the magnets.