[susan53]

It always, always, always depends on the context - you can never decide from a single sentence. Grammar is meaning - different forms give us the chance to express different semantic concepts (which you yourself point out), so the choice of form depends entirely on the meaning that the speaker wishes to express. So here for instance :

- past simple verbs express the idea that an event is finished, over and done with. Is this what the speaker wants to imply? Eg in this example, the speaker wants to emphasise that the previous agreement is no longer valid - it's "over and done with":
A : Are you helping with the Sports Day on Friday?
B . No.
A: David thinks you are.
B: Yes, well... I agreed to do it previously, but my mother's in hospital and I have to go and visit her. I haven't seen David recently so he doesn't know. I must phone him.

Here, the agreement is finished - it's no longer valid, so s/he chooses the sinmple past.

Some authentic examples, all from the BBC website .

Weapons that they previously agreed not to create in exchange for aid.
...some member countries still fall short of criteria they previously agreed to.
They now blame the UK government for turning a blind eye to an issue they initially agreed to defend.

The present perfect, on the other hand, combines past and present. So if an agreement made in the past is still valid in the present, the speaker may choose that form. In this example, the speaker is emphasising that the past agreement still holds in the present:

A: OK, Can I start the meeting by summarising the things that we have previously agreed to do? And then we'll move on. We said that we would use a third of the budget...

Some authenitic examples from the BBC and British Government websites :

The US has previously agreed there can be no further easing of relations between the two countries until he is released.
Unless the licensing section has previously agreed in writing that an alternative scale plan is acceptable the ...
Mr Bashir has previously agreed to the existing AU force being beefed up, but questions such as the size of the force and who would lead it have not yet been settled.
...most of the parties have initially agreed and there is a potential developer on board

You always need to look at the meanings expressed by the form and then ask what meaning the speaker/writer wanted to convey in that specific situation. it's that which will govern the choice of form.