The Near Earth Asteroid Rendezvous (NEAR) spacecraft flew within 3830 kilometers of asteroid 433 Eros on 23 December 1998. The gravitational perturbation on NEAR was evident in the spacecraft tracking data. Ground-based Doppler and range tracking of the spacecraft as well as spacecraft images of the asteroid's center of figure and surface features were used to determine the mass and rotation pole of Eros. The mass of Eros is (7.2 +/- 1.8) x 10(18) grams and, coupled with a volume estimate provided by the NEAR imaging team, this mass suggests a bulk density of 2.5 +/- 0.8 grams per cubic centimeter. The rotation pole position is 15.6 (+/-3.7) degrees in right ascension and 16.4 (+/-1.8) degrees in declination, which is consistent with ground-based and NEAR imaging team observations.