The short answer to this question is of course, "Yes". The Prophet Isaiah cited this fact as one of the unique attributes of God:
"Remember the former things of old: for I am God, and there is none else; I am God, and there is none like me, declaring the end from the beginning, and from ancient times the things that are not yet done, saying, My counsel shall stand, and I will do all my pleasure" (Isaiah 46:9-10).
There are two issues that are raised with regard to the question of God's foreknowledge: 1). Does this mean that all things are predetermined by God? 2). Why then does God allow evil to happen, when He foresees it?
Before we get to those two questions, however, we should consider the question of how God knows the future. Does He know the future because He makes it happen in a particular way? According to Orthodox theology, He knows the future because He is uncircumscribed, i.e., He is not limited by time or space. The Wisdom of Sirach says "His gaze spans all the ages; to Him there is nothing unexpected" (Ecclesiasticus 39:20). God sees the future, because He is not limited, is already in the future, and at the same time transcends time.
As for the claim that foreknowledge requires that God determine all things, there is no logical reason why this is so. Furthermore, the fact is that the Church has always rejected any notion of determinism. St. John of Damascus wrote, in his Exact Exposition of the Orthodox Faith:
"We ought to understand that while God knows all things beforehand, yet He does not predetermine all things. For He knows beforehand those things that are in our power, but He does not predetermine them. For it is not His will that there should be wickedness nor does He choose to compel virtue. So that predestination is the work of the divine command based on foreknowledge. But on the other hand God predetermines those things which are not within our power in accordance with His foreknowledge. For already God in His foreknowledge has prejudged all things in accordance with His goodness and justice" (Exact Exposition of the Orthodox Faith, 2:30).
For more on this issue, see "Dialogue on Free Will and Determinism."
With regard to the question of why, if God knows the future, He does not prevent evil is essentially the same question you would have to ask even if God did not know the future, because one doesn't have to know the future to know that people with evil intentions will likely accomplish evil, if they are allowed to proceed with their plans unhindered. But in both cases, God would have to regularly violate our free will to prevent us from doing evil.
For more on that issue, see "The Problem of evil".
