Yes, almost certainly this is enough. If more is needed, it would be to give more detail to make it clear what we agreed - for example, when we agreed, or what we agreed about. I don't think you need to add to/on/upon.
1. agree to-- be ready to; The General Manager has agreed to attend the function.
2. agree with-- in agreement with (a person); I agree with you that the ...
3. agree upon-- concede to (statements etc) ; After the meeting, we have agreed upon the 2nd and 5th points.