Why has God created us? The Almighty Lord does not need anyone; he does not need the angels, the heaven, or the earth. Are there any written words in the Bible that tell the reason?
There are two ways to look at this, and there are arguments to both, so there isn't a correct answer that can be proven as it depends on how you want to interpret Scripture, since we are trying to understand God's motivation for creation, which is similar to an ant trying to understand our motivation for doing something.
You may want to read through this article, as I think this author did a fantastic job of explaining some of the relatively early church fathers thoughts on this, with references.
Since this paper does such a fantastic job, I will show three sections that may help to at least show the two sides, but start with the fact that God is necessary, and perfect, so he doesn't have to create in order to be perfect.
Augustine had one side, which was that God could not fail to create, but Thomas Aquinas took the other side that God had the freedom to create or not create, so the freedom of indifference.
If God chose not to create, would that make him any less that He is?
If God is perfect, why does He need our worship/love/adoration (whatever He gets from us)?
Regardless of God's reason for creating us, the end result is that we exist because of God's Love and Greatness.
But, I do enjoy the simplicity that was in this blog: http://michellewui.blog.co.uk/2011/03/23/the-reason-that-god-created-man-10877315/
In Ezekial 18:4 we have:
God created us so we can have an eternal relationship with him, though, as seen in Genesis, with the Trinity already existing, God was not alone, so He didn't do it because He was lonely, but the idea that we were created to be able to know Him and by knowing Him deeply we can spend all of eternity with him is a fantastic idea.
Her simplicity is very nice, and since the OT asked about Bible verses I thought this would at least meet that requirement.
For the interested reader, I dug out my trusty copy of Scriptural References for the Baltimore Catechism. For Lesson 1 (The Purpose of Man's Existence), Question 3 (Why did God make us? Answer: God made us to show forth His goodness and to share with us His everlasting happiness in heaven.), the references are:
a. Ecclesiasticus 17:1-10 After a description of God's creation of man the author states that God "set His eyes upon their hearts to show them the greatness of His works."
b. Matthew 25:34-35 The just are called to posses the kingdom prepared for them
c. 1 Corinthians 8:8-12 St. Paul points out that after this life we shall see God "face to face".
d. Revelation 21:3-4, 22:3-5 John describes the Heavenly Jerusalem where the servants of God will see His face.
The answer is along the lines of "because it pleased him." God is creative -- that's reason enough to create, even for us humans!
There's an answer on GotQuestions.org that's more elaborate and includes some relevant Bible passages, too.