All of the players on the field participate in the final penalty shootout. The order is determined by your formation, with one exception: subs shoot first, in last in first out order.
I just played a Single Player Tournament, and manufactured a tie break shootout by ensuring a 0 - 0 score at the end of extra time.
I then recorded each shooter in order, and tried to prolong the shootout for as long as I could. My team shot in the following order:
If you compare this shot order with my formation, the answer becomes immediately apparent.
It looks like the order is determined much like one reads a book. The front rank shoots first, beginning with the member furthest to the left. When he is done shooting, the player to his right in the formation shoots next. This continues down the line to the end, where it begins again for the second rank, and again for the third.
Update: I played another shoot out, and I noticed that my subs shoot first, with the last person to join the game shooting first. Once the subs had shot, then the order proceeded as detailed above.
Also note: In yet another shootout, I attempted to manipulate the order, by moving players to different positions at the end of extra time. This "substitution" was ignored by the game. The players shot in accordance with their positions on the field at the end of extra time.