This is the first version of a complete near-IR point source catalogue towards the Magellanic Clouds extracted from the data obtained with the DEep Near Infraread Survey of the Southern Sky (DENIS). The catalogue covers an area of 19.87x16 square degrees centered on (05:27:20-69:00:00) for the Large Magellanic Cloud (LMC), and 14.7x10 square degrees centered on (01:02:40-73:00:00) for the Small Magellanic Cloud (SMC). It contains the sources detected in at least 2 of the 3 photometric bands I (Gunn-i centered at 0.8{mu}m), J (centered at 1.25{mu}m), and K_s_ (centered at 2.15{mu}m). The spatial resolution is 1" in I and 3" in the J and K bands, and the limiting magnitudes are I=18, J=16 and K_s_=14. 70% of the detected sources are real members of the Magellanic Clouds, and consist mainly of red giants, asymptotic giant branch stars and supergiants.