Why is “agreed” used as an interjection?

When you use "Agreed" as an interjection, it is equivalent to "I agree." It is short for the much more formal "It is agreed."

One way you typically see this done is when speakers are setting the ground rules (or baseline assumptions) before beginning a discussion where there may be some disagreement.

This likely stems from a more formal era where you were making an oral contract with somebody, and the first speaker declares the terms of the contract, and the second speaker is accepting the terms of the contract. "It is agreed that we will proceed the way we have discussed." Over time this has just been shortened to "Agreed" which then morphed into a simple way of showing agreement.

It just is.

And the Oxford English Dictionary gives usages as far back as 1534

1534 J. Heywood Play of Loue sig. Bi, Loued not louyng. We shall neuer agre Unlesse ye wyll admyt some man..to..gyue iudgement. Louer not loued. Agred.

This old usage just shows a different spelling of agreed (as for love, lover, loved, etc.)

I think of it as the second party indicating that the two parties are agreed (in agreement) when the second party says agreed. Either that or the matter at hand has been agreed upon with the second party saying agreed.

It could have first had a legal connotation in that the oldest meaning of agreement was a legal term akin to contract.

We can just think of it as the equivalent of I agree.

Agreed is used to express your approval on the immediate matter at hand, and is thus welcome in an oral discussion with friends or when instant-messaging someone. For instance:

What do you say we go out and grab a drink after work ?
Agreed !

Used this way, you could replace it with a simple "Okay !" or "Alright !"

You wouldn't use it so much in a discussion on a forum or through emails, and would prefer I agree to show someone you and him have the same point of view.