Simply put, they are those that God chose to save before the foundation of the world,
Eph 1:3 Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places,
Eph 1:4 even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love
Eph 1:5 he predestined us for adoption through Jesus Christ, according to the purpose of his will,
Eph 1:6 to the praise of his glorious grace, with which he has blessed us in the Beloved.
Eph 1:7 In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace,
Eph 1:8 which he lavished upon us, in all wisdom and insight
Eph 1:9 making known to us the mystery of his will, according to his purpose, which he set forth in Christ
Elect means chosen, chosen means elect
All believers are elect, and all the elect will be believers in time.
You are right the elect are mentioned all thru the NT, all believers in the OT were elect too.
Thats what the majority of Baptist churches have taught and believed thru history, many do not teach it now, you may not have ever heard a sermon about it because alot of churches won't preach the whole counsel of God, when you consider that it is one of the most prevalent doctrines in the Bible, you would think some would preach it by accident, and alot of times they do and then try to explain it away, why would someone want to explain away the wisdom of God?