There is no verse in the Bible that says "love conquers all." However, there are verses and chapters in the Bible that come close in terms of meaning, including Romans 8:37, 1 Corinthians 13, 1 Peter 4:8 and Matthew 22:36-40.
The phrase "love conquers all" is derived from the following phrase in the Latin poet Virgil's Eclogues X.69: "Omnia vincit amor et nos cedamus amori." It means "love conquers all, let us all yield to love." The beginning of the phrase was subsequently translated as "love conquers all" by Geoffrey Chaucer, an English poet of the Middle Ages, and thereafter passed into popular usage.