John Piper on knowing God versus being known by God:
But in [1 Corinthians 8:3] Paul does not simply relate loving God to knowing as we ought to know. He says, ‘But if anyone loves God, he is known by God.’ What is the point of saying, ‘He is known by God’? This is parallel to Galatians 4:9: ‘But now that you have come to know God, or rather to be known by God, how can you turn back again to the weak and worthless elementary principles of the world?’
Deeper than knowing God is being known by God. What defines us as Christians is not most profoundly that we have come to know him but that he took note of us and made us his own.
Being known by God is another way of talking about election—God’s freely choosing us for himself, in spite of our not deserving it. It the kind of knowing referred to in Amos 3:2: ‘You only have I known of all the families of the earth.’ God had chosen Israel as his people, though they were no better than any others.
What Paul is doing when he says, ‘If anyone loves God, he is known by God.’ Is reminding the proud Corinthians that loving God, not loveless knowledge, is the sign of being among the elect. He is reminding them that everything they have is owing to God’s free and sovereign initiative.
John Piper, Think: The Life of the Mind and the Love of God (Wheaton, IL: Crossway, 2010), 160-161.