Desiderio

In a casual game, a card you choose from outside the game comes from your personal collection. In a tournament event, a card you choose from outside the game must come from your sideboard. In Limited events, your sideboard includes an arbitrary number of basic lands. You may look at your sideboard at any time.

You choose the card to play from outside the game at the time you are playing it, not at the time Wish resolves.

You still need to pay all costs to play a card this way, and you must follow all normal timing rules.