Abstract: The measurement of the internal Rn-222 activity in the NEXT-White detector during the so-called Run-II period with Xe-136-depleted xenon is discussed in detail, together with its implications for double beta decay searches in NEXT. The activity is measured through the alpha production rate induced in the fiducial volume by Rn-222 and its alpha-emitting progeny. The specific activity is measured to be (38.1 +/- 2.2 (stat.) +/- 5.9 (syst.)) mBq/m(3). Radon-induced electrons have also been characterized from the decay of the Bi-214 daughter ions plating out on the cathode of the time projection chamber. From our studies, we conclude that radon-induced backgrounds are sufficiently low to enable a successful NEXT-100 physics program, as the projected rate contribution should not exceed 0.1 counts/yr in the neutrinoless double beta decay sample.