According to ODO the adjectival agreed is sufficient:
1.0 Discussed or negotiated and then accepted by all parties:
the agreed date
1.1 (Of two or more parties) holding the same view or opinion on something:
all the republics are agreed on the necessity of a common defence policy
The Learner's Dictionary concurs with added explanation:
3 of two or more people or groups : to decide to accept something
after discussing what should or might be done
— usually + on or upon
- The jurors were unable to agree on a verdict. [=to reach a verdict]
- agree on a plan
- They agreed on a fair division of the profits.
[+ object] (Brit)
- The jurors were unable to agree a verdict.
- The means of ending the dispute were finally agreed.
◊ The forms agreed, agreed-upon, and (less commonly) agreed-on are
used as adjectives in both U.S. and British English.
- She paid him the agreed price.
- They met at the agreed-upon time.
Agreed upon is preferred in legal language for a binding contractual arrangement:
constituted or contracted by stipulation or agreement; "stipulatory
WordNet 3.0 Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
The dominance of agreed upon in the corpus, seems to be rooted in formal, regulatory and legal usage. The connotation of legal consistency may give native speakers a greater sense of accuracy with agreed upon.