This paper provides expressions to be used to implement the new definition of UT1 corresponding to the IAU 2000 resolutions either in the new (CEO-based) or classical (equinox-based) transformations between the International Terrestrial Reference System (ITRS) and the Geocentric Celestial Reference System (GCRS). The new expression for Greenwich Sidereal Time (GST) has to be in agreement at the micro-arcsecond level, for one century, with the IAU 2000 expressions for the Earth Rotation Angle (ERA) and for the quantity s positioning the Celestial Ephemeris Origin (CEO) on the equator of the CIP. The computations of the new expressions using the IAU 2000 precession-nutation model are performed in such a manner as to ensure that there is no discontinuity in UT1 on 1 January 2003 and that there is equivalence of the classical and new transformations between the ITRS and GCRS relative to the rotation about the axis of the CIP when these expressions are used. The equinox offset that is considered in the computations refers to the dynamical mean equinox of J2000.0. The resulting expressions have been included in the IERS Conventions 2000.