Chasal Siddur Pesach was written in 11th-century Germany by Yosef Tov Elem. We often understand it as meaning, “The Seder is completed appropriately, with all its laws and practices. . . . ”. However, this is mistaken. 

The poem was originally intended to be recited on the Shabbat prior to Passover, when it is customary to learn about the holiday and become familiar with its laws and practices. Therefore, it is not the Seder which we have finished - but studying the siddur of Pesach, that is, the order of the proceedings (from the same root as Seder, of course), before the event itself.

Chasal Siddur Pesach really means, “We have completed an appropriate preparation (i.e., knowing everything’s order) of the laws and practices of Passover,” but not the actual execution of the laws and practices themselves. This is why the poem ends with, “Just as we have merited to order it, so too shall we merit to execute it,” bringing together our ordering intent with practice -- when it was originally sung, the Seder was still ahead.

haggadah Section: Nirtzah