The principal recommendations of this Report on the system of astronomical constants are in accordance with the resolutions passed at Symposium no. 21 (Paris, May 1963). We first of all give a reference list of the constants of the system and a set of explanatory notes. We have used the term ‘primary constant’, rather than ‘fundamental constant’, since the latter has a connotation in astronomical usage that is inappropriate to the manner of selection of the primary constants. In choosing the values for the primary constants we have, perhaps, adopted a conservative view of the likely errors of their determinations, but even so the new system should be of adequate accuracy for astronomical studies for many years. Limits within which the true values are believed to lie are indicated in a later section, in which we also give expressions for differential corrections to the derived constants. Finally we discuss the manner in which this system should be introduced into the national and international ephemerides.