What is actually involved depends upon the nature of the dispensation and the level to which one need have recourse.
There are dispensations I grant orally…such as the Friday abstinence, the fasts in Lent, or the Sunday obligation. Usually, before granting the dispensation, I will propose first a commutation. Other times, I will choose simply to go straight to dispensation. It varies upon the situation.
I have never formulated quite the way you have. If oral, I will either say, typically, in the active voice “I grant the dispensation” or in the passive voice “The dispensation is granted.” From time to time, I will be asked to put it in writing.
In issues regarding marriage or ordination, a decree would be issued by competent ecclesiastical authority for inclusion with the paperwork kept on file, as proof that the dispensation had been sought by appropriate petition and that it had been duly obtained.
As one proceeds up the ladder, if recourse is needed to the Holy See for example, the decree is typically more elaborate.