  We present here a nearly complete census of classical Cepheids in the
Magellanic System. The sample extends the set of Cepheids published in the past
by the Optical Gravitational Lensing Experiment (OGLE) to the outer regions of
the Large (LMC) and Small Magellanic Cloud (SMC). The entire collection
consists of 9535 Cepheids of which 4620 belong to the LMC and 4915 are members
of the SMC. We provide the I- and V-band time-series photometry of the
published Cepheids, their finding charts, and basic observational parameters.
  Based on this unique OGLE sample of Cepheids we present updated
period--luminosity relations for fundamental, first, and second mode of
pulsations in the I- and V-bands and for the W_I extinction-free Wesenheit
index. We also show the distribution of classical Cepheids in the Magellanic
System. The OGLE collection contains several classical Cepheids in the
Magellanic Bridge - the region of interaction between the Magellanic Clouds.
The discovery of classical Cepheids and their estimated ages confirm the
presence of young stellar population between these galaxies.
