Lots of mis-information floating around out there, so I thought I'd try and clarify. The MLB Collective Bargaining Agreement can be found here (in case you want to read it for yourself).
The CBA, Article (XX) Section (B) Paragraph (3) entited "Rights of Club" states:
If the Player accepts the offer to arbitrate, he shall be a signed player for the next season and the parties will conduct a salary arbitration proceeding under Article VI; provided, however, that the rules concerning maximum salary reduction set forth in Article VI shall be inapplicable and the parties shall be required to exchange figures on the last day established for the exchange of salary arbitration figures under Article VI. The Club shall be deemed not to have signed a free agent for purposes of paragraph (5) of this Section B when a Player accepts salary arbitration pursuant to this paragraph (3).
The key point here being that the player is not considered a free agent signing.
Article (XX) Section (B) Paragraph (6) entitled "Miscellaneous" sub-paragraph(a) states:
Any Club signing a contract after the expiration of the election period with a Player under this Section B may not assign his contract until after the next June 15. However, notwithstanding the foregoing, such contract may be assigned for other Player contracts and/or cash consideration of $50,000 or less prior to the next June 16 if the Player gives written consent to such transaction.
The first sentence does not apply to our case since it refers to Free Agent signings, or the signing of a contract after arbitration expiration. The second paragraph, however, does apply. I read this as to mean that a player who has agreed to arbitration can be traded but only with his written consent.
So, in summary, I was initially wrong by saying that Soriano can be traded immediately upon completion of his contract (and I have posted that in more than one thread so please ignore it). Gondeee's 12/7 11am update on the Soriano thread is accurate with the exception of the date, which is actually June 16.