On the morning of 1 June 1978 the First Presidency and the Quorum of the Twelve Apostles met in the upper room of the Salt Lake Temple. By the accounts later given by those present, Spencer W. Kimball, then president of the church, put the question to the quorum after long private prayer, and the assembled leaders reported a shared and unmistakable confirmation that the restriction should end. The decision was announced publicly on 9 June 1978 in a letter from the First Presidency stating that all worthy male members might be ordained without regard to race or colour, and that temple blessings were available to all. It was presented to a general conference on 30 September 1978 and sustained, and it stands in the Doctrine and Covenants as Official Declaration 2.
What the announcement did not do was explain the restriction. For thirty-five years the church left the explanations of the past standing by not repudiating them, and they continued to circulate in manuals, in seminary classes and in family conversation. That ended in December 2013, when the church published its Gospel Topics essay on race and the priesthood. The essay states that the restriction began under Brigham Young, that no revelation is known to have established it, and that the church disavows the theories advanced in the past, naming among them the ideas that Black skin is a sign of divine disfavour or a curse, and that people were less valiant in a premortal life. It condemns all racism, past and present.
The essay is the tradition's own account and is cited here as such. It is also, by any reading, an unusual document for a church to publish about itself.