At the very beginning of Act V, we see Ariel and Prospero discussing the success of their plan. In fact, Ariel suggests that the plan and Prospero's magic have had far stronger effects than they first anticipated. Ariel states:
Your charm so strongly works 'em
That if you now beheld them, your affections
Would become tender.
In short, Ariel states that if Prospero took the time to look at the castaways he would feel sorry for them and take pity on them. Prospero considers this idea and then states that because of his "nobler reason" he believes "the rarer action is / In virtue than in vengeance."
And because they are sorry for their prior sins and he has accomplished his goals, Prospero then orders:
Go release them, Ariel:
My charms I'll break, their senses I'll restore,
And they shall be themselves.