Quick answer: The correct term is “hear, hear.”

The Maven’s word of the day answered this question back in 1998: The shout is hear, hear.

They continue:

The original form of this expression was hear him, which was usually repeated. This imperative was used to call attention to a speaker’s words, and naturally developed the sense of a broad expression of favor.

… As a parliamentary cheer, hear him, hear him! is first recorded in the late seventeenth century and continued into the nineteenth; the reduction to hear! or hear, hear! occurred by the late eighteenth century. However, the use of the verb hear as an imperative meaning ‘listen!’ is older: a notable example is the parliamentary-sounding “Then cried a wise woman out of the city, Hear, hear” (King James Bible, 2 Samuel xx 16).

The Straight Dope agrees:

When you agree with someone, do you say “Here Here!” or “Hear Hear” ? And what does it mean? What is the origin of “Here Here” or “Hear Hear”?

— Tymoma195

The answer: The correct term is, “hear, hear!” It is an abbreviation for “hear, all ye good people, hear what this brilliant and eloquent speaker has to say!”