We present B, V and I CCD light curves for 101 variable stars belonging to the globular cluster NGC2419, 60 of which are new discoveries, based on datasets obtained at the TNG, SUBARU and HST telescopes. The sample includes 75 RR Lyrae stars (of which 38 RRab, 36 RRc and one RRd), one Population II Cepheid, 12 SX Phoenicis variables, 2 DeltaScuti stars, 3 binary systems, 5 long-period variables, and 3 variables of uncertain classification. The pulsation properties of the RR Lyrae variables are close to those of Oosterhoff type II clusters, consistent with the low metal abundance and the cluster horizontal branch morphology,disfavoring (but not totally ruling out) an extragalactic hypotesis for the origin of NGC2419. The observed properties of RR Lyrae and SX Phoenicis stars are used to estimate the cluster reddening and distance, using a number of different methods. Our final value is mo(NGC2419)=19.71+/-0.08mag (D= 87.5+/-3.3kpc), with E(B-V)=0.08+/-0.01mag, [Fe/H]=-2.1dex in the Zinn & West metallicity scale, and a value of Mv that sets mo(LMC)=18.52mag. This value is in good agreement with most recent literature estimates of the distance to NGC 2419. ; Comment: 26 pages, 16 figures, 4 tables; accepted for publication in AJ