As explained by R' Avigdor Nebenzahl in his book, Tik'u ba-Chodesh Shofar: Thoughts for Rosh haShanah (page 240), it was David who "chose" Jerusalem, and prayed that his choice be accepted by HaShem. When HaShem made it clear that this choice was, indeed, accepted, it was essentially an acknowledgement that HaShem "chose" Jerusalem.
I suppose a cynic could argue that David should not have made a decision without clear instructions from HaShem, or that his doing so meant that HaShem didn't really choose Jerusalem in fulfillment of the verse. But I think that a)history (and the Bible) has shown that this was, in fact, the fulfillment of the verse, in that Jerusalem has been acknowledged by billions of people around the world as G-d's Holy city ever since, and b)without a direct prophecy saying otherwise, it seems G-d was "happy" with this choice.
Many things in TaNa"Ch, not to mention events throughout history, and even in our own lives, ultimately retrospectively are revealed to have been the Will of G-d, even if He didn't directly say so. I don't know why this has to be any different. He "chose" Jerusalem when it was ready to be chosen.
Did He "know" that He would later "choose" Jerusalem?* I think it was very likely*, as Jewish tradition also tells us that Jerusalem was regarded by Shem as perfect, as well as the place that HaShem told Avraham to go to offer his son Yitzhak. It is also identified by some (though not all) commentaries as the place where Ya'akov had his dream about the angels on the ladder.
If there weren't something special about Jerusalem, I don't think it would have stood the test of prophecy and time.
*(Broadly speaking, I think, questions about G-d's future knowledge are outside the scope of this particular question. My wording is meant as a plain-language answer without getting into those deeper philosophical issues.)