I wouldn't say Jesus is the book of life.BTW, Jesus Himself is God's Book of Life.
If YOU ARE in Him, then you ARE IN the Book of Life.
Its all about HIS Life, not yours or mine!!
So, to answer your question, God's Book of Life, that we may enter in, IS JESUS, by His first appearance.
If you are not IN Jesus (born again), before He bodily returns from Heaven, then know that you are NOT in the Book of Life, aka "the kingdom of God" . John 3:3-8
Revelation 3:5 He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels.
Revelation 13:8 And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world.Revelation 21:27And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.