What authority is the constitution established by?

"We the people" is the subject of the sentence, and thus the authority that is ordaining and establishing.

So basically, we did it. Or the we that existed then. :)

This is the text of the preamble:

"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America."